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Temporal Constraints: A Survey
Abstract
Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about temporal occurrences and temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. path-consistency) and (ii) enhancing naive backtracking search.
... REPRESENTING and managing temporal knowledge is an essential task in many areas, including planning, scheduling, humanmachine interaction, natural language understanding, diagnosis, and robotics. Different approaches have been developed, ranging from general-purpose approaches, like Hidden Markov Models, Bayesian Networks, or logical approaches, to more specific approaches focusing on constraint satisfaction problems, and on temporal constraints (see, e.g., the surveys in [1], [2], [3]). The latter approaches (which are the focus of this paper) can be distinguished on the basis of whether they focus on the qualitative or quantitative temporal constraints. ...
... The literature shows that temporal reasoning and query answering are closely related tasks: correct query answering can be provided only if temporal reasoning evaluates the tightest temporal constraints. Indeed, computing the tightest constraints is a fundamental task, to which a lot of efforts have been devoted in the literature [1], [2], [3], [5], [6]. ...
... As most approaches focusing on quantitative constraints (see [1], [2], [3]), we base our approach on the notion of distance between time points. A preference is associated to each distance. ...
Representing and managing temporal knowledge, in the form of temporal constraints, is a crucial task in many areas, including knowledge representation, planning, and scheduling. The current literature in the area is moving from the treatment of “crisp” temporal constraints to fuzzy or probabilistic constraints, to account for preferences and\or uncertainty. Given a set of temporal constraints, the evaluation of the tightest implied constraints is a fundamental task, which is essential also to provide reliable query-answering facilities. However, while such tasks have been widely addressed for “crisp” temporal constraints, they have not attracted enough attention in the “non-crisp” context yet. We overcome such a limitation, by (i) extending quantitative temporal constraints to cope with preferences, (ii) defining a temporal reasoning algorithm which evaluates the tightest temporal constraints, and (iii) providing suitable query-answering facilities based on it.
... This explains, why temporal representation and reasoning services are so important and appear in so many areas, including planning, natural language understanding, and knowledge representation. Recent articles describe approaches in the area of Temporal Constraint Programming, an important area of temporal reasoning (Schwalb and Vila 1998;Gennari 1998). Gennari describes a temporal reasoning system as a temporal knowledge base. ...
... To compute a solution, backtracking search is used. It has been shown that the search gets more effective with the additional use of path-consistency as a forward-checking method within the backtracking algorithm (Schwalb and Vila 1998). These mentioned arguments hold also for the Semantic Web. ...
... Other authors such as(Schwalb and Vila 1998) describe these three main streams as metric point (for metric information), qualitative point and qualitative interval (for qualitative approaches based on Allen's interval algebra), and combinations (for mixed approaches). ...
The Bremen University Semantic Translator for Enhanced Retrieval (BUSTER) follows the idea of the Semantic Web annotating information sources with metadata following some kind of formalization. It is an ontology-based pro-totype that helps applications or users to (a) find the needed information and (b) integrate and/or translate this information for further processes. So far, a logic-based approach for terminological reasoning and a graph-based approach for rea-soning about place names have been developed (concept@location). Another important part of search is time dependent: e.g. people are looking for hotels in areas at a certain time (e.g. during summer vacation) using common terms rather than to specify time according to the machine-oriented W3C stan-dard. This paper deals with both annotation and reasoning issues about temporal knowledge based on the Semantic Web. We developed a new time representation scheme based on Allen's time intervals and Freksa's semi-intervals. We also de-veloped and implemented a temporal reasoner enabling us to check the temporal model and to derive new temporal knowledge. This takes us to a new type of query: concept@location in time. An example is given to demonstrate the perfor-mance of our approach.
... Allen in his work [3] formulated thirteen relationship principles that express all Since then, much work has been conducted to detect, extract, and represent such temporal information. Examples are [28,50,58,97,98,135,147]. These research endeavors represent the trend of discovering events and temporal relationships from temporal data. ...
... Since then, much work has been conducted to detect, extract, and represent such temporal information. Examples are [28,50,58,97,98,135,147]. These works represent the trend of discovering events and temporal relationships from temporal data. ...
... These orderings describe how events between data streams relate. Research, such as [50,58,97,98,135], has focused on processing numerical or descriptive univariate, multivariate, or symbolic temporal data with the goal of discovering events and temporal relationships from temporal data. Others have explored the discovery of temporal knowledge and associated patterns, such as [54,71,100]. ...
... Actions are unordered and lifted by default; constraints are added to T and B where necessary to impose temporal orderings, ground variables and remove conflicts. By changing the language of implementation of T , a number of qualitative and quantitave temporal models can be implemented with varying complexity and expressiveness (Schwalb and Vila, 1998;Dechter et al., 1991). ...
... The first disadvantage may partially be dealt with by providing the merger agent with an expressive planning formalism and flexible plan merging algorithms enabling it to resolve a wide 17 A Conditional Simple Temporal Network is a variant of the well known Simple Temporal Network (Schwalb and Vila, 1998) that uses labels on nodes to represent the branches of a plan in which the relevant timepoints exist. range of possible conflicts. ...
... These orderings describe how events relate. Research, such as [15,20,33,43], has focused on processing numerical or descriptive univariate, multivariate, or symbolic temporal data with the goal of discovering events and temporal relationships from temporal data. Others have explored the discovery of temporal knowledge and associated patterns, such as [17,24,34]. ...
... Other research [12,35] has explored the concept of breaking temporal events into core units of beginnings and endings through S-I temporal ordered processing. Previously mentioned research ( [1,20,33,43]) has investigated patterns and relations among interval data irrespective of the data being ordinal or nominal. ...
This paper investigates a technique for the discovery of temporal behavior models within multimedia event data. Advancements in both technology and the marketplace present us the opportunity for research in analysis of situated human behavior using video and other sensor data (media streams). By situated analysis, we mean the study of behavior in time as opposed to looking at behavior in the form of aggregated data divorced from how they occur in context. Human and social scientists seek to model behavior captured in media, and these data may be represented in a multi-dimensional event data space derived from media streams. The knowledge of these scientists (experts) is a valuable resource which can be leveraged to search this space. We propose a solution that incorporates the expert in an iteratively, interactive data-driven discovery process to evolve a desired behavior model. We test our solution's accuracy on a multimodal meeting corpus with a progressive three tiered approach.
... Additionally, if a complex task needs multiple UAVs at the same time, it could be represented by a simultaneous constraint. For more details, a representation of the time interval constraints is well organized in [29]. Temporal constraints on the relations between two tasks are represented in algebraic forms. ...
Task allocation is an essential element for determining the capability of multi-UAV systems to perform various tasks. This paper presents a procedure called a “rebalancing algorithm” for generating task-performing routes in heterogeneous multi-UAV systems. The algorithm adopts a greedy-based heuristic approach to find solutions efficiently in dynamically changing environments. A novel variable named “loitering” is introduced to satisfy temporal constraints, resulting in improved performance compared to heuristic algorithms: a sequential greedy algorithm, a genetic algorithm, and simulated annealing. The rebalancing algorithm is divided into two phases to minimize the makespan, i.e., the initial allocation and reallocation phases. Simulation results demonstrate the proposed algorithm’s effectiveness in highly constrained conditions and its suitability for heterogeneous systems. Additionally, the results show a reduction in calculation time and improved performance compared to the heuristic algorithms.
... For more details about temporal reasoning, the interested reader is referred to (Vila 1994;Schwalb and Vila 1998;Bartak, Morris, and Venable 2014). ...
In this paper we give a structural characterization and extend the tractability frontier of the Simple Temporal Problem (STP) by defining the class of the Extended Simple Temporal Problem (ESTP), which augments STP with strict inequalities and monotone Boolean formulae on inequations (i.e., formulae involving the operations of conjunction, disjunction and parenthesization). A polynomial-time algorithm is provided to solve ESTP, faster than previous state-of-the-art algorithms for other extensions of STP that had been considered in the literature, all encompassed by ESTP. We show the practical competitiveness of our approach through a proof-of-concept implementation and an experimental evaluation involving also state-of-the-art SMT solvers.
... Such frameworks can be used as specialised knowledge servers to which temporal problems can be demanded, to solve complex tasks (e.g., planning, and scheduling) in an efficient and compositional way. The AI special-purpose approaches on temporal constraints have been traditionally divided into two main classes, depending on whether they deal with quantitative or qualitative temporal constraints (see, e.g., the surveys in (Barták et al., 2014;Schwalb & Vila, 1998;Terenziani, 2006;Vila, 1994)). Quantitative temporal constraints involve metric time and include dates (e.g., "Mary was enrolled on 10/1/2020"), delays (e.g., "Sue was enrolled 15 days after Mary"), and durations (e.g., "Mary worked for the company XXX for 120 days"). ...
Knowledge-based decision support systems have a long tradition within the medical area. In particular, in the last decades, many Computer-Interpretable Guidelines (CIG) systems have been built to provide evidence-based and knowledge-based support to physicians. Since CIGs are, by definition, devoted to the management of specific diseases, the treatment of comorbid patients constitutes a challenging task in the area, involving (i) the detection of the possible interactions between (the effects of) the actions recommended by multiple CIGs (one for each disease of the patient), (ii) the management of such interactions and, finally, (iii) the conciliation of (the recommendations of) different CIGs. This paper focuses on issue (i) above, and specifically, on an innovative approach to support interaction detection along the temporal dimension. Practically, interactions can only occur between effects that intersect in time. Therefore, interaction detection involves the representation of temporal information (temporal constraints), and temporal reasoning (to propagate such constraints). Additionally, query answering facilities are important to support physicians in the investigation of the results of temporal reasoning. Current CIG approaches that face such issues take into account only “crisp” temporal constraints, i.e., they consider all temporal constraints as equally probable\preferred. However, preferences about the temporal constraints between CIGs actions may be available, as well as knowledge about the probabilistic distribution of the effects of CIGs actions in time. Considering such additional pieces of information can provide crucial advantages, in term of the flexibility and informativeness of the support provided by the CIG system to physicians. In this paper, we propose the first homogeneous approach to represent and reason with (propagate) temporal constraints with both preferences and probabilities. We ground our approach on the widely-used Simple Temporal Problem (STP) framework, which supports temporal reasoning on temporal constraints about possible distances between events. We extend (i) the representation formalism to associate preferences and\or probabilities to the possible distances, and (ii) the operations to propagate the constraints to combine also preferences and probabilities. We also (iii) provide an experimental evaluation of our approach, and (iv) propose a wide range of query-answering supports, to facilitate physicians in the analysis of the results of temporal reasoning in general, and in the temporal detection of possible interactions in particular. Finally, (v) we also show how such a temporal framework is integrated in GLARE-SSCPM, a CIG system to treat comorbid patients, and show the advantages of our approach considering a running example.
... Temporal constraint networks are among the most refined models for modeling and solving temporal problems [18,19], including dynamic controllability checking. A temporal constraint network is dynamically controllable if it is possible to determine a schedule that, given the activities executed so far, incrementally determines which activities can be started (and for the controllable ones, their duration) to satisfy all the temporal constraints. ...
This paper presents TimeAwareBPMN-js, a graphical web-based editor for time-aware BPMN (Business Process Model and Notation) models that allows (1) creating and editing of BPMN processes enriched with temporal constraints, such as contingent durations and conditions, and (2) verifying that such constraints are well-defined and satisfy some (temporal) properties. The verification of temporal constraints is realized by plug-ins that can be easily added by the user thanks to the modular architecture of the application. Different plug-ins may verify different temporal properties. As a proof-of-concept, TimeAwareBPMN-js contains the CSTNU plug-in which verifies the dynamic controllability property, i.e., it checks, at design-time, whether there exists a run-time schedule for the process that satisfies all temporal constraints no matter how contingent durations and conditions are revealed during execution.
... For more details about temporal reasoning, the interested reader is referred to (Vila 1994;Schwalb and Vila 1998;Bartak, Morris, and Venable 2014). ...
In this paper we give a structural characterization and extend the tractability frontier of the Simple Temporal Problem (STP) by defining the class of the Extended Simple Temporal Problem (ESTP), which augments STP with strict inequalities and monotone Boolean formulae on inequations (i.e., formulae involving the operations of conjunction, disjunction and parenthesization). A polynomial-time algorithm is provided to solve ESTP, faster than previous state-of-the-art algorithms for other extensions of STP that had been considered in the literature, all encompassed by ESTP. We show the practical competitiveness of our approach through a proof-of-concept implementation and an experimental evaluation involving also state-of-the-art SMT solvers.
... These constraints may arise from the business policies, common practices and mutual agreements between business partners related to efficiency and productivity requirements in business practices. The key BP constraints described in the literature (Lu et al., 2009;Schwalb and Vila, 1998;Marjanovic and Orlowska, 1999;Roman and Kifer, 2007) can be mapped to one of the following constraint types: ...
Purpose
This paper reviews existing business process (BP) modeling languages that are widely used in the industry as well as recent research work on modeling and analysis of BPs in the service-oriented environment and Internetware-based software paradigm. BPs in such environment are different from traditional BPs due to loose coupling of partner services, dynamic and on-the-fly selection of partners and run-time process adaptability. The unique characteristics of these BPs require formal modeling of the requirements and constraints in each phase of their life cycle, including design phase, implementation and deployment phase and execution phase.
Design/methodology/approach
The paper first provides a categorization of typical user requirements in each phase of the BP life cycle. Then a detailed comparison of the selected languages with respect to their requirement modeling and analysis capabilities in each of the identified categories is provided. The paper also discusses new requirements engineering research challenges arising from future software needs and emerging trends in software engineering in the context of Web-services-based BPs and Internetware.
Findings
There is a need to have a framework that provides support for user requirements modeling and analysis for all the phases of BP life cycle in an integrated manner. Such a framework would be useful not only in resolving the inconsistencies between requirements across phases but also in addressing the issues related to BP evolution due to changes in user requirements over time. Moreover, with the Internet of things (IoT) adoption in BPM, there is a need to have an integrated environment that provides support for capturing the resilience requirements of enterprise BPs as well as the mobility constraints of the underlying IoT devices.
Originality/value
This paper reviews existing BP modeling languages and frameworks and discusses the new requirements engineering research challenges arising from future software needs and the emerging trends in BP management in the service-oriented environment and Internetware-based software paradigm.
... Temporal constraint satisfaction and deciding consistency tasks have been widely studied from different perspectives that range from data management to computational intelligence and knowledge representation [16]. However, to the best of our knowledge, there is no previous work about random interval graphs that formalizes and analyzes the data consistency of Linked Data sources and the Semantic Web. ...
Concern about the propagation of fake news and data grows every day. At the same time, the analysis and mining of large data sets have become essential in the decision-making processes, in which incorrect data bring misleading insights. However, there is no general-purpose, automatic mechanism to effectively ensure the consistency of temporal data in Linked Data sources such as Wikidata, Wikimedia's free knowledge base.
In this paper, an approach based on cross-comparing date values to discover inconsistent data is proposed. Besides, the concept of contemporary constraint, on which this approach is based, is defined and formalized in order to show how to find inconsistencies in a wide range of data sources. Our experimental results show that contemporary constraints are effective and can be used with multiple purposes for data curation and data quality analysis. As a success story, the contemporary constraint has been implemented in Wikidata.
... A TR is a sequence of temporal conditions that should hold in order for a temporal result to be produced ( Barták, Morris, & Venable, 2014 ). Furthermore, certainty factors are used in order to declare the certainty of specific rule parts ( Allen, 1983;Schwalb & Vila, 1998 ). Bellow we define in details the parts which are used to construct a rule. ...
The huge diversity and quantity of data and information, and the requirements for knowledge extraction out of them put new challenges for knowledge management, synthesis, conflict detection and reasoning This paper elaborates on the design and development of COSMOS, an intelligent system which supports a) collaboration of experts for developing common knowledge bases and b) diagnosis derivation which takes into account time and uncertainty. The health domain is used for illustration and discussion of the features of our approach. Initially, we present the syntax and the semantics of the rules which incorporate time (temporal rules) and the data items upon which reasoning is performed. Then we introduce its inference engine, able to perform reasoning on top of rules and data, handling also the embedded time and uncertainty. We proceed further to define a conflict detection policy for supporting the difficult and error prone task of rule generation. The complexities of the aforementioned tasks are hidden from users via a well-designed and user friendly web interface that possesses strong collaboration features enabling multiple experts to work on defining a rule and on developing a common knowledge base. Evaluation of COSMOS has been performed using a) students studying expert systems and b) health experts in order to demonstrate the usability of the approach and the considerable advantages gained. To the best of our knowledge, COSMOS is one of the very few systems combining temporal rules, a powerful inference engine handling uncertainty and conflict detection and progresses beyond state of the art by adopting strong collaboration features and paradigms.
... This algebra is obtained by assuming that all the endpoints of intervals are distinct. By this way, seven of the Allen's relations are eliminated and the remaining ones are: <, >, o, o i , d, d i .The reader may refer to[32] for a survey of the constraint satisfaction problem (CSP) algorithms while Krokhin et al. provide a complete classification of the computational complexity of the algorithms of satisfiability of the IA[33]. ...
In this paper, we present a review of the existing temporal models in the literature. More precisely, we review the models that handle temporal relations between intervals, between points or between intervals and points. The existing temporal models are categorized based on which type of information they handle. Three categories of temporal models are identified: qualitative temporal models, quantitative temporal models or hybrid temporal models. Once temporal information is represented, some reasoning methods about time will be presented in order to give a glance about how temporal information is processed.
... A third type of network called the point-duration network (PDN) is used to reason about durations [11,42,46,69]. The reader may refer to [55] for a survey of the constraint satisfaction problem (CSP) algorithms while Krokhin et al. provide a complete classification of the computational complexity of the algorithms of satisfiability of the IA [34]. ...
The context of this work is to characterize the content and the structure of audiovisual documents by analysing the temporal relationships between basic events resulted from different segmentations of the same document. For this objective, we need to represent and reason about time. We propose a parametric representation of temporal relation between segments (points or intervals) in which the parameters are used to characterize the relationship between two non-convex intervals corresponding to two segmentations in the video analysis domain. The relationship is represented by a co-occurrences matrix noted as Temporal Relation Matrix (TRM). Each document is represented by a set of TRMs computed between each couple of segmentations of the same document using different features. The TRMs are analysed later to detect semantic events, highlight clues about the video content structure or to classify documents based on their types. For higher-level semantic events and documents’ structure, we needed to apply some operations on the basic temporal relations and TRMs such as composition, disjunction, complement, intersection, etc. These operations brought to light more complex patterns; e.g. event 1 occurs at the same time of event 2 followed by event 3. In the work presented in this paper, we define a temporal relation algebra including its set of operations based on the parametric representation and TRM defined above. Several experimentations have been done on different audio and video documents to show the efficiency of the proposed representation and the defined operations for audiovisual content analysing.
... When we add time to the problem, then we have a temporal constraint satisfaction problem (TCSP). It is a particular class of CSP where variables represent times (time points, time intervals or durations) and constraints establish allowed temporal relations between them [25]. ...
Management and mission planning over a swarm of unmanned aerial vehicle (UAV) remains to date as a challenging research trend in what regards to this particular type of aircrafts. These vehicles are controlled by a number of ground control station (GCS), from which they are commanded to cooperatively perform different tasks in specific geographic areas of interest. Mathematically the problem of coordinating and assigning tasks to a swarm of UAV can be modeled as a constraint satisfaction problem, whose complexity and multiple conflicting criteria has hitherto motivated the adoption of multi-objective solvers such as multi-objective evolutionary algorithm (MOEA). The encoding approach consists of different alleles representing the decision variables, whereas the fitness function checks that all constraints are fulfilled, minimizing the optimization criteria of the problem. In problems of high complexity involving several tasks, UAV and GCS, where the space of search is huge compared to the space of valid solutions, the convergence rate of the algorithm increases significantly. To overcome this issue, this work proposes a weighted random generator for the creation and mutation of new individuals. The main objective of this work is to reduce the convergence rate of the MOEA solver for multi-UAV mission planning using weighted random strategies that focus the search on potentially better regions of the solution space. Extensive experimental results over a diverse range of scenarios evince the benefits of the proposed approach, which notably improves this convergence rate with respect to a naïve MOEA approach.
... Expressive and efficient temporal reasoning is essential to a number of areas in Artificial Intelligence (AI) [8,14,15]. Over the past few years, many constraint-based formalisms have been developed to represent and reason about time in automated planning and temporal scheduling [4,12]. ...
In 2005 T.K.S. Kumar studied the Restricted Disjunctive Temporal Problem (RDTP), a restricted but very expressive class of Disjunctive Temporal Problems (DTPs). An RDTP comes with a finite set T = {X, Y,. . .} of temporal variables, and a finite set C of temporal constraints each of which can be of either one of the following three types: (t 1) (Y − X ≤ w), for w real (a simple temporal difference constraint); (t 2) (l 1 ≤ X ≤ u 1) ∨ · · · ∨ (l k ≤ X ≤ u k), for l i , u i reals (a single-variable disjunction of many interval constraints); (t 3) (l 1 ≤ X ≤ u 1) ∨ (l 2 ≤ Y ≤ u 2), for l i , u i reals (a two-variable disjunction of two interval constraints only). Kumar showed that RDTPs are solvable in deterministic strongly-polynomial time by reducing them to the Connected Row-Convex (CRC) constraints problem, also, he devised a faster randomized algorithm. Instead, the most general form of DTPs allows for multi-variable disjunctions of many interval constraints and it is NP-complete. This work offers a deeper comprehension on the tractability of RDTPs, leading to an elementary deterministic strongly-polynomial time algorithm for solving them, significantly improving the asymptotic running times of all the previous deterministic and randomized algorithms. The result is obtained by reducing RDTPs to the Single-Source Shortest-Paths (SSSP) and the 2-SAT problem (jointly), instead of reducing to CRCs. In passing, we obtain a faster (quadratic time) algorithm for RDTPs having only {t 1 , t 2 }-constraints (and no t 3-constraint). As a second main contribution, we study the tractability frontier of solving RDTPs blended with Hyper Temporal Networks (HyTNs), a strict generalization of Simple Temporal Networks (STNs) grounded on hypergraphs: we prove that solving temporal problems having only t 2-constraints and either only multi-tail or only multi-head hyperarc-constraints lies in NP ∩ co-NP and admits deterministic pseudo-polynomial time algorithms; on the other hand, problems having only t 3-constraints and either only multi-tail or only multi-head hyperarc-constraints are strongly NP-complete.
... General qualitative reasoning is covered by, for instance, the collection edited by Weld and de Kleer (1990) and the survey article by Dague (1995), while qualitative constraints is the topic of the textbook by Ligozat (2013). There are also two wellknown surveys concerning temporal and spatial reasoning by Schwalb and Vila (1998) and , respectively. ...
Qualitative reasoning formalisms are an active research topic in artificial intelligence. In this survey we present a model-theoretic perspective on qualitative constraint reasoning and explain some of the basic concepts and results in an accessible way. In particular, we discuss the significance of ω-categoricity for qualitative reasoning, of primitive positive interpretations for complexity analysis, and of Datalog as a unifying language for describing local consistency algorithms.
... A CSP consists of a set of variables V = v 1 , ..., v n , each one with a finite set of possible values D i (its domain), and a set of constraints C i restricting the values that variables can simultaneously take. Moreover, the MPP must consider the time when the tasks in the mission start and end, so a particular class of CSP called Temporal Constraint Satisfaction Problem (TCSP) [5], where variables represent times (time points, time intervals or durations) and constraints represent sets of allowed temporal relations between them, must be considered. ...
From the last few years the interest and repercussion on Unmanned Aerial Vehicle (UAV) technologies have been extended from pure military applications to industrial and societal applications. One of the basic tasks to any UAV problems is related to the Mission Planning. This problem is particularly complex when a set of UAVs is considered. In the field of Multi-UAV Mission Planning, some approaches have been carried out in the last years. However, there are few works related to real-time Mission Replanning, which is the focus of this work. In Mission Replanning, some changes in the mission, such as the arrival of new tasks, require to update the preplanned solution as fast as possible. In this paper a Multi-Objective Genetic Algorithm for Mission Replanning (MOGAMR) is proposed to handle this problem. This approach uses a set of previous plans (or solutions), generated using an oa liffline planning process, in order to initialize the population of the algorithm, then acts as a complete regeneration method. In order to simulate a real-time system we have fixed a time limit of 2 minutes. This has been considered as an appropriate time for a human operator to take a decision. Using this time restriction, a set of experiments adding from 1 to 5 new tasks in the Replanning Problems has been carried out. The experiments show that the algorithm works well with this few number of new tasks during the replanning process generating a set of feasible solutions under the time restriction considered.
... A TCSP is a particular class of CSP where variables represent times (time points, time intervals, or durations) and constraints represent sets of allowed temporal relations between them (Schwalb and Vila 1998). Different classes of constraints are characterized by the underlying set of basic temporal relations (BTR). ...
Due to recent booming of unmanned air vehicles (UAVs) technologies, these are being used in many fields involving complex tasks. Some of them involve a high risk to the vehicle driver, such as fire monitoring and rescue tasks, which make UAVs excellent for avoiding human risks. Mission planning for UAVs is the process of planning the locations and actions (loading/dropping a load, taking videos/pictures, acquiring information) for the vehicles, typically over a time period. These vehicles are controlled from ground control stations (GCSs) where human operators use rudimentary systems. This paper presents a new multi-objective genetic algorithm for solving complex mission planning problems involving a team of UAVs and a set of GCSs. A hybrid fitness function has been designed using a constraint satisfaction problem to check whether solutions are valid and Pareto-based measures to look for optimal solutions. The algorithm has been tested on several datasets, optimizing different variables of the mission, such as the makespan, the fuel consumption, and distance. Experimental results show that the new algorithm is able to obtain good solutions; however, as the problem becomes more complex, the optimal solutions also become harder to find.
... Temporal reasoning is an important field of artificial intelligence as evidenced by continual developments and growing number of applications [49]. Temporal reasoning operates on a formal representation of time and provides a means to reason about temporal aspects of knowledge [50,51]. There are two main ways of representing temporal information. ...
Computer simulation programs are essential tools for scientists and engineers to understand a particular system of interest. As expected, the complexity of the software increases with the depth of the model used. In addition to the exigent demands of software engineering, verification of simulation programs is especially challenging because the models represented are complex and ridden with unknowns that will be discovered by developers in an iterative process. To manage such complexity, advanced verification techniques for continually matching the intended model to the implemented model are necessary. Therefore, the main goal of this research work is to design a useful verification and validation framework that is able to identify model representation errors and is applicable to generic simulators.
The framework that was developed and implemented consists of two parts. The first part is First-Order Logic Constraint Specification Language (FOLCSL) that enables users to specify the invariants of a model under consideration. From the first-order logic specification, the FOLCSL translator automatically synthesizes a verification program that reads the event trace generated by a simulator and signals whether all invariants are respected. The second part consists of mining the temporal flow of events using a newly developed representation called State Flow Temporal Analysis Graph (SFTAG). While the first part seeks an assurance of implementation correctness by checking that the model invariants hold, the second part derives an extended model of the implementation and hence enables a deeper understanding of what was implemented. The main application studied in this work is the validation of the timing behavior of micro-architecture simulators. The study includes SFTAGs generated for a wide set of benchmark programs and their analysis using several artificial intelligence algorithms. This work improves the computer architecture research and verification processes as shown by the case studies and experiments that have been conducted.
... Par conséquent, si nous considérons (c s , C T ) i la paire de contraintes spatiales et temporelles associée au faisceau i, le défi de l'algorithme est de trouver le faisceau qui satisfait l'ensemble des contraintes ou qui minimise les fonctions de modélisation de ces contraintes. [Schwalb et Vila, 1998] Pour mieux aborder les paragraphes ci-dessous, nous avons proposé la définition d'une notation d'une cellule hexagonale dans notre structure de données. Soit une cellule (i, j) définie dans le graphe, sa notation est la suivante : ...
De nos jours, les applications informatiques autonomes sont au centre de grandes préoccupations de la recherche scientifique. Ces dernières sont destinées initialement à des systèmes d'aide à la décision dans des environnements contraints et dynamiques, communément appelés environnements complexes. Elles peuvent dès à présent, à l'aide des avancées de la recherche, permettre de construire et déduire leurs connaissances propres afin d'interagir en temps réel avec leur environnement. Cependant, elles sont confrontées à la difficulté d'avoir une modélisation fidèle du monde réel et des entités qui le composent. L'un des principaux objectifs de nos recherches est de capturer et modéliser la sémantique associée aux entités spatio-temporelles afin d'enrichir leur expressivité dans les SIG ou les systèmes d'aide à la décision. Un service de routage maritime dynamique a été déployé en exploitant cette modélisation. Cet algorithme a été démontré comme optimal en termes d'espace mémoire et de temps de calcul. La sémantique capturée se compose de l'affordance et de la saillance visuelle de l'entité spatiale. Les connaissances associées à cette sémantique sont par la suite représentées par une ontologie computationnelle qui intègre des approches spatio-temporelles. Ces connaissances sont soit déduites du savoir de l'expert du domaine, soit extraites de gros volumes de données textuelles en utilisant des techniques de traitement automatique du langage. L'ontologie computationnelle proposée nous a permis de définir un algorithme de routage maritime dynamique (fonction des évènements ou objets présents dans l'environnement) fondé sur une heuristique itérative monocritère de plus courte distance et bidirectionnelle. L'algorithme BIDA* proposé s'applique sur un graphe itératif qui est une conceptualisation d'une grille hexagonale itérative recouvrant la zone de navigation. Cet algorithme permet aussi la gestion de différents niveaux de résolution. Toujours dans l'initiative de produire un modèle aussi proche que possible du monde réel, l'algorithme BIDA* a été enrichi des stratégies multicritères afin de prendre en compte les différentes contraintes de la navigation maritime. Les contraintes globales et locales auxquelles nous nous sommes intéressés sont la profondeur des eaux, la distance de navigation et la direction de navigation. Le modèle proposé permet ainsi d'enrichir les capacités cognitives des utilisateurs évoluant dans les environnements maritimes et peut aussi être utilisé pour construire des systèmes complètement autonomes explorant ces environnements. Un prototype expérimental de navigation intelligente mettant en oeuvre cette modélisation et proposant un service de routage maritime a été développé dans le cadre de cette thèse.
... – m i {b} j si max i < min j ; – m i {m} j si max i = min j ; – m i {o} j si min i < min j , max i > min j et max i < max j ; – m i {s} j si min i = min j et max i < max j ; – m i {d} j si min i > min j et max i < max j ; – m i {f} j si min i > min j et max i = max j ; – m i {eq} j si min i = min j et max i = max j ; – m i {r } j si m j {r} i, avec r défini par p = pi, m = mi, o = oi, s = si, d = di et f = fi. [20]. Ce test de cohérence est NP-complet [28]. ...
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed. Qualitative interval algebras can model processes using finer temporal relations, but they cannot reproduce all workflow patterns. This paper defines a common ground model-theoretical semantics for both workflows and interval algebras, making it possible for reasoning systems working with either to interoperate. Thanks to this, interesting properties and inferences can be defined, both on workflows and on an extended formalism combining workflows with interval algebras. Finally, similar formalisms proposing a sound formal basis for workflows and extending them are discussed.
... A Temporal Constraint Satisfaction Problem (TCSP) is a particular class of CSP where variables represent times (time points, time intervals or durations) and constraints represent sets of allowed temporal relations between them [15]. Different classes of constraints are characterized by the underlying set of Basic Temporal Relations (BTR). ...
The Multi-UAV Cooperative Mission Planning Problem (MCMPP) is a complex problem which can be represented with a lower or higher level of complexity. In this paper we present a MCMPP which is modelled as a Constraint Satisfaction Problem (CSP) with 5 increasing levels of complexity. Each level adds additional variables and constraints to the problem. Using previous models, we solve the problem using a Branch and Bound search designed to minimize the fuel consumption and number of UAVs employed in the mission, and the results show how runtime increases as the level of complexity increases in most cases, as expected, but there are some cases where the opposite happens.
... Actions are-93 - unordered and lifted by default; constraints are added to T and B where necessary to impose temporal orderings, ground variables and remove conflicts. By changing the language of implementation of T[102], a number of qualitative and quantities temporal models can be implemented with varying complexity and expressiveness[103].A causal link is a structure a i ⎯→ ⎯ l a j where a i and a j are actions in A, a i is ordered before a j and l is an effect of ai and a precondition of a j . a i and a j are referred to as the provider and consumer of the literal respectively. ...
In recent years, urban traffic congestion and air pollution have become huge problems in many cities in the world. In order to reduce congestion, we can invest in improving city infrastructures. Infrastructure improvements, however, are very costly to undertake and do not reduce air pollution. Hence we can work on intelligent mobility in order to have a more efficient car use. The application of new information technologies, such as multi-agent technologies to urban traffic information control, has made it possible to create and deploy more intelligent traffic management like DRT (Demand Responsive Transport) system. The objective of multi-agent based DRT system is to manage taxis in an intelligent way, to increase the efficient number of passengers in every vehicle, and at the same time to decrease the number of vehicles on streets. This will reduce the CO2 emissions and air pollution caused by the vehicles, as well as traffic congestion and financial costs. Multi-agent simulation has been looked as an efficient tool for urban dynamic traffic services. However, the main problem is how to build an agent-based model for it. This research presents a multi-agent based demand responsive transport (DRT) services model, which adopts a practical multi-agents planning approach for urban DRT services control that satisfies the main constraints: minimize total slack time, client's special requests, increases taxis' seats use ratio, and using minimum number of vehicle etc. In this thesis, we propose a multi-agent based multi-layer distributed hybrid planning model for the real-time problem. In the proposed method, an agent for each vehicle finds a set of routes by its local search, and selects a route by cooperation with other agents in its planning domain. By computational experiments, we examine the effectiveness of the proposed method. This research is supported by project "Gestion Temps Réel du Transport Collectif à la Demande" (CPER) Budgetthe French.
... The challenge of the computational algorithm is to find the beam which satisfies the set of constraints or minimizes the functions modelling these constraints. Regarding the temporal constraint satisfaction problem, Schwalb and Vila (1998) define it like a computational solution to represent and perform queries on temporal occurrences and relations. Borrmann et al. (2009) distinguishes three different types of spatial constraints: distance constraint (distance, closerThan, fartherThan and maxDist), directional constraints (above, below, northOf, southOf, eastOf, westOf) and topological constraints (disjoint, meet, overlap, cover, coveredBy, contain, equal and inside). ...
Route planning is an important problem for many real-time applications in open and complex environments. The maritime domain is a relevant example of such environments where dynamic phenomena and navigation constraints generate difficult route finding problems. This paper develops a spatial data structure that supports the search for an optimal route between two locations while minimizing a cost function. Although various search algorithms have been proposed so far (e.g. breadth-first search, bidirectional breadth-first search, Dijkstra's algorithm, A(*), etc.), this approach provides a bidirectional dynamic routing algorithm which is based on hexagonal meshes and an iterative deepening A(*) (IDA(*)) algorithm, and a front to front strategy using a dynamic graph that facilitates data accessibility. The whole approach is applied to the context of maritime navigation, taking into account navigation hazards and restricted areas. The algorithm developed searches for optimal routes while minimizing distance and computational time.
... For modelling and solving the temporal aspects of planning and scheduling problems, quantitative temporal constraint networks in the form of the Simple Temporal Problem (STN) are widely adopted. Schwalb & Vila (1998) survey the wider work on temporal constraint satisfaction, including qualitative and hybrid formulations. ...
Table of contents Workshop on Constraint Programming for
... A TCSP is a particular class of CSP where variables represent times (time points, time intervals or durations) and constraints represent sets of allowed temporal relations between them [15]. A UAS mission can be perfectly represented as a set of temporal constraints over the time the tasks in the mission start and end. ...
Mission Planning is a classical problem that has been traditionally studied in several cases from Robotics to Space missions. This kind of problems can be extremely difficult in real and dynamic scenarios. This paper provides a first analysis for mission planning to Unmanned Air Vehicles (UAVs), where sensors and other equipment of UAVs to perform a task are modelled based on Temporal Constraint Satisfaction Problems (TCSPs). In this model, a set of resources and temporal constraints are designed to represent the main characteristics (task time, fuel consumption, ...) of this kind of aircrafts. Using this simplified TCSP model, and a Branch and Bound (B&B) search algorithm, a set of feasible solutions will be found trying to minimize the fuel cost, flight time spent and the number of UAVs used in the mission. Finally, some experiments will be carried out to validate both the quality of the solutions found and the spent runtime to found them.
... To stop the problem becoming excessively complicated, the temporal relationships are restricted in siblings under the AND node in the task tree, that is, if task A and B are siblings under OR nodes or from different parents, then there are no direct temporal constraints upon them. The temporal constraints used are qualitative interval constraints and qualitative interval-point constraints [47]. ...
The tasks would fail to be assigned to any robots in the task allocation phase as a consequence of the inherent communication constraints in multi-robot systems (MRS). This negative effect becomes even more serious in tasks with temporal constraints. We therefore propose the constraint-based approach (CoBA), a market-based task allocation approach to enable multi-robot coordination in domains with temporal constraints between subtasks of a complex task and network constraints between robots. We handle network constraints by having each robot maintain a dynamic acquaintance network of robots that it knows about, and allowing a robot to submit a bid on behalf of another robot during a task auction ("indirect bidding"). In order to model the complex task, we introduce the AND/OR task tree with temporal constraints. An auction-clearing routine, which supports the AND/OR task tree with temporal constraints and direct/indirect task auction, is proposed to enable effective multi-robot task allocation in spite of various constraints. The solution was validated in both simulation and physical environments by a series of experiments in disaster response domains. Specifically, we study the system performance by separately varying the number of robots, the expected rate of task issuance, the communication reliability factor, the compositions of MRS, as well as the acquaintance relationship parameter, in simulation experiments. The results suggest that our solution outperforms others, that is, robots were able to complete the tasks more promptly and effectively.
... A TCSP is a particular class of CSP where variables represent times (time points, time intervals or durations) and constraints represent sets of allowed temporal relations between them [34]. Different classes of constraints are characterized by the underlying set of basic temporal relations (BTR). ...
The problem of Mission Planning for a large number of Unmanned Air Vehicles (UAV) can be formulated as a Temporal Constraint Satisfaction Problem (TCSP). It consists on a set of locations that should visit in different time windows, and the actions that the vehicle can perform based on its features such as the payload, speed or fuel capacity. In this paper, a temporal constraint model is implemented and tested by performing Backtracking search in several missions where its complexity has been incrementally modified. The experimental phase consists on two different phases. On the one hand, several mission simulations containing (n) UAVs using different sensors and characteristics located in different waypoints, and (m) requested tasks varying mission priorities have been carried out. On the other hand, the second experimental phase uses a backtracking algorithm to look through the whole solutions space to measure the scalability of the problem. This scalability has been measured as a relation between the number of tasks to be performed in the mission and the number of UAVs needed to perform it.
... It is widely accepted that spatial reasoning plays a central role in various artificial intelligence applications. As in the case of other qualitative reasoning formalisms (e.g., qualitative temporal reason- ing [4, 26] ), spatial reasoning can be viewed under different, somehow complementary, points of view. We distinguish between the algebraic level, that is, purely existential theories formulated as constraint satisfaction problems (CSP s) [31] over jointly exhaustive and mutually disjoint set of topological, directional based, or combined relations, the first-order level, that is, first-order theories of topological, directional based, or combined relations, and the modal logic level, where a (usually propositional) modal language is interpreted over opportune Kripke structures representing space. ...
Qualitative spatial representation and reasoning plays a important role in various spatial applications. In this paper we introduce a new formalism, we name RCD calculus, for qualitative spatial reasoning with cardinal direction relations between regions of the plane approximated by rectangles. We believe this calculus leads to an attractive balance between efficiency, simplicity and expressive power, which makes it adequate for spatial applications. We define a constraint algebra and we identify a convex tractable subalgebra allowing efficient reasoning with definite and imprecise knowledge about spatial configurations specified by qualitative constraint networks. For such tractable fragment, we propose several polynomial algorithms based on constraint satisfaction to solve the consistency and minimality problems. Some of them rely on a translation of qualitative networks of the RCD calculus to qualitative networks of the Interval or Rectangle Algebra, and back. We show that the consistency problem for convex networks can also be solved inside the RCD calculus, by applying a suitable adaptation of the path-consistency algorithm. However, path consistency can not be applied to obtain the minimal network, contrary to what happens in the convex fragment of the Rectangle Algebra. Finally, we partially analyze the complexity of the consistency problem when adding non-convex relations, showing that it becomes NP-complete in the cases considered. This analysis may contribute to find a maximal tractable subclass of the RCD calculus and of the Rectangle Algebra, which remains an open problem.
... Allen in [2] formulated thirteen relationship principles to express all the possible ordering relationships between two interval events. Much work has been conducted to detect, extract, and represent such temporal information, e.g., [7,10,21,22,31,33]. ...
The analysis of multimodal data benefits from meaningful search and retrieval. This paper investigates strategies of searching multimodal data for event patterns. Through three longitudinal case studies, we observed researchers exploring and identifying event patterns in multimodal data. The events were extracted from different multimedia signal sources ranging from annotated video transcripts to interaction logs. Each researcher's data has varying temporal characteristics (e.g., sparse, dense, or clustered) that posed several challenges for identifying relevant patterns. We identify unique search strategies and better understand the aspects that contributed to each.
The interpretation process is one of the main tasks performed by archaeologists who, starting from ground data about evidences and findings, incrementally derive knowledge about ancient objects or events. Very often more than one archaeologist contributes in different time instants to discover details about the same finding and thus, it is important to keep track of history and provenance of the overall knowledge discovery process. To this aim, we propose a model and a set of derivation rules for tracking and refining data provenance during the archaeological interpretation process. In particular, among all the possible interpretation activities, we concentrate on the one concerning the dating that archaeologists perform to assign one or more time intervals to a finding to define its lifespan on the temporal axis. In this context, we propose a framework to represent and derive updated provenance data about temporal information after the mentioned derivation process. Archaeological data, and in particular their temporal dimension, are typically vague, since many different interpretations can coexist, thus, we will use Fuzzy Logic to assign a degree of confidence to values and Fuzzy Temporal Constraint Networks to model relationships between dating of different findings represented as a graph-based dataset. The derivation rules used to infer more precise temporal intervals are enriched to manage also provenance information and their following updates after a derivation step. A MapReduce version of the path consistency algorithm is also proposed to improve the efficiency of the refining process on big graph-based datasets.
Artificial intelligence largely relies on bounds on differences (BoDs) to model binary constraints regarding different dimensions, such as time, space, costs, and calories. Recently, some approaches have extended the BoDs framework in a fuzzy, “noncrisp” direction, considering probabilities or preferences. While previous approaches have mainly aimed at providing an optimal solution to the set of constraints, we propose an innovative class of approaches in which constraint propagation algorithms aim at identifying the “space of solutions” (i.e., the minimal network) with their preferences, and query answering mechanisms are provided to explore the space of solutions as required, for example, in decision support tasks. Aiming at generality, we propose a class of approaches parametrized over user‐defined scales of qualitative preferences (e.g., Low, Medium, High, and Very High), utilizing the resume and extension operations to combine preferences, and considering different formalisms to associate preferences with BoDs. We consider both “general” preferences and a form of layered preferences that we call “pyramid” preferences. The properties of the class of approaches are also analyzed. In particular, we show that, when the resume and extension operations are defined such that they constitute a closed semiring, a more efficient constraint propagation algorithm can be used. Finally, we provide a preliminary implementation of the constraint propagation algorithms. Example of a bound on differences with layered preferences representing the possible distances between points P1 and P2, and the qualitative preferences over such distances.
This chapter is devoted to three representative applications of PSO in operations research. Similarly to the previous chapters, our attention is focused on the presentation of essential aspects rather than reviewing the existing literature. Thus, we present methodologies for formulation of the optimization problem, which is not always trivial, as well as for the efficient treatment of special problem requirements that cannot be handled directly by PSO. Under this prism, we report applications from the fields of scheduling, inventory optimization and game theory. Recent results are also reported per case to provide an idea of the efficiency of PSO.
The treatment of patients affected by multiple diseases (comorbid patients) is one of the main challenges of the modern healthcare, involving the analysis of the interactions of the guidelines for the specific diseases. However, practically speaking, such interactions occur over time. The GLARE project explicitly provides knowledge representation, temporal representation and temporal reasoning methodologies to cope with such a fundamental issue. In this paper, we propose a further improvement, to take into account that, often, the effects of actions have a probabilistic distribution in time, and being able to reason (through constraint propagation) and to query probabilistic temporal constraints further enhances the support for interaction detection.
Over the last decade, developments in unmanned aerial vehicles (UAVs) has greatly increased, and they are being used in many fields including surveillance, crisis management or automated mission planning. This last field implies the search of plans for missions with multiple tasks, UAVs and ground control stations; and the optimization of several objectives, including makespan, fuel consumption or cost, among others. In this work, this problem has been solved using a multi-objective evolutionary algorithm combined with a constraint satisfaction problem model, which is used in the fitness function of the algorithm. The algorithm has been tested on several missions of increasing complexity, and the computational complexity of the different element considered in the missions has been studied.
The huge diversity, big quantity of data and information, and the requirements for knowledge extraction out of them put new challenges for knowledge management, synthesis, conflict detection and reasoning. In this paper, we present COSMOS, a knowledge system that fully addresses these challenges, in an efficient way, paving the way for a new generation of knowledge systems. Using our approach, it is possible for domain experts to generate temporal knowledge rules. As those rules are saved to our knowledge base, a conflict detection mechanism detects and solves rule conflicts. Then, an inference engine is able to perform efficiently, accurate decisions, based on available factual information using reasoning and handling uncertainty. Ontologies are used to model both the factual information and the data items in the rules enabling also interoperability with existing systems. To validate our approach, as an application scenario, we deploy our infrastructure in a health environment where doctors provide rules that are activated over a patient health record. Preliminary results indicate the benefits of our approach for decision support based on health data, successfully identifying adverse events and enabling intelligent patient monitoring.
A novel framework for mining temporal association rules by discovering itemsets with frequent itemsets tree is introduced. In order to solve the problem of handling time series by including temporal relation between the multi items into association rules, a frequent itemsets tree is constructed in parallel with mining frequent itemsets to improve the efficiency and interpretability of rule mining without generating candidate itemsets. Experimental results show that our algorithm can provide better efficiency and interpretability in mining temporal association rules in comparison with other algorithms and has good application prospects.
Temporal reasoning, in the form of propagation of temporal constraints, is an important topic in Artificial Intelligence. The current literature in the area is moving from the treatment of "crisp" temporal constraints to fuzzy or probabilistic constraints, to account for different forms of uncertainty and\or preferences. However, despite the huge amount of work in the area, the spectrum of possible solutions has not been fully explored. In particular, no probabilistic approach coping with quantitative temporal constraints has been proposed yet. We overcome such a limitation of the current literature by proposing the first approach providing (i) a probabilistic extension to quantitative constraints, supporting the possibility of expressing alternative distances between time points, and of associating a probability to each alternative, and (ii) a framework for the propagation of such temporal constraints.
Workflow temporal verification is conducted to guarantee on-time completion, which is one of the most important QoS (Quality of Service) dimensions for business processes running in the cloud. However, as today's business systems often need to handle a large number of concurrent customer requests, conventional response-time based process monitoring strategies conducted in a one-by-one fashion cannot be applied efficiently to a large batch of parallel processes because of significant time overhead. Similar situations may also exist in software companies where multiple software projects are carried out at the same time by software developers. To address such a problem, based on a novel runtime throughput consistency model, this paper proposes a QoS-aware throughput based checkpoint selection strategy, which can dynamically select a small number of checkpoints along the system timeline to facilitate the temporal verification of throughput constraints and achieve the target on-time completion rate. Experimental results demonstrate that our strategy can achieve the best efficiency and effectiveness compared with the state-of-the-art as and other representative response-time based checkpoint selection strategies. Copyright
A systematic approach for modeling and verifying timing constraints was developed to ensure timing constraints in the real-time systems. The approach defines the basic time concepts and gives a timing constraint model based on the simple temporal problem-improved (STP-I) method. A verification algorithm is given for consistence checking of the constraint graph model using a constraint resolver. A transformation mechanism is also given to transform complex timing constraints to basic expressions. A case study of a real-time data process unit (DPU) system illustrates the approach. This approach gives a more systematic analysis of typical fault models for real-time systems than existing designs, hence it can model the constraints more accurately using the concepts of time points and time intervals that facilitate effective time defect detection.
Real-time tasks need attributes for monitoring their execution and performing recovery actions in case of failures. Temporal constraints are a class of real-time task attributes where the constraints relate the status of the task to temporal entities. Violating temporal constraints can produce consequences of unknown severity. This paper is part of our on-going research on real-time multi agent systems constraints. We discuss the importance of temporal constraints and present a task model that explicitly represents temporal constraints. We also present our preliminary results from our initial implementation in the domain of Meeting Schedules Management involving multiple users assisted by agents.
Allen's interval algebra is one of the best established formalisms for temporal reasoning. This article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra. When the constraints are chosen from the full Allen's algebra, this form of satisfiability problem is known to be NP-complete. However, eighteen tractable subalgebras have previously been identified; we show here that these subalgebras include all possible tractable subsets of Allen's algebra. In other words, we show that this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NP-complete. We obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras, and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property.
The purpose of the paper is to compare timed and time Petri nets with constraint satisfaction problems and activity-on-arc graphs in the context of manufacturing. It is shown that constraints are not defined in the same way but that timed and time Petri nets could be translated into a set of activity-on-arc graphs. This translation is only straightforward for p-timed and p-time Petri nets.
On-time completion is one of the most important QoS (Quality of Service) dimensions for business processes running in the cloud. While today’s business systems often need to handle thousands of concurrent user requests, process monitoring is basically conducted in a one by one fashion. It is possible to repeat the strategies for monitoring a single process a thousand times to monitor a thousand parallel processes. However, the time overhead will be a thousand-fold increase as well, which brings a big challenge for process monitoring. In this paper, based on a novel runtime throughput consistency model, we propose a QoS-aware throughput based checkpoint selection strategy which can dynamically select a small number of checkpoints along the system timeline to facilitate the temporal verification of throughput constraints and achieve the target on-time completion rate. The experimental results demonstrate that our strategy can achieve the best efficiency and effectiveness compared with the state-of-the-art as well as other representative response-time based checkpoint selection strategies.
Scientific processes are usually time constrained with overall deadlines and local milestones. In scientific workflow systems, due to the dynamic nature of the underlying computing infrastructures such as grid and cloud, execution delays often take place and result in a large number of temporal violations. Since temporal violation handling is expensive in terms of both monetary costs and time overheads, an essential question aroused is “do we need to handle every temporal violation in scientific workflow systems?” The answer would be “true” according to existing works on workflow temporal management which adopt the philosophy similar to the handling of functional exceptions, that is, every temporal violation should be handled whenever it is detected. However, based on our observation, the phenomenon of self-recovery where execution delays can be automatically compensated for by the saved execution time of subsequent workflow activities has been entirely overlooked. Therefore, considering the nonfunctional nature of temporal violations, our answer is “not necessarily true.” To take advantage of self-recovery, this article proposes a novel adaptive temporal violation handling point selection strategy where this phenomenon is effectively utilised to avoid unnecessary temporal violation handling. Based on simulations of both real-world scientific workflows and randomly generated test cases, the experimental results demonstrate that our strategy can significantly reduce the cost on temporal violation handling by over 96% while maintaining extreme low violation rate under normal circumstances.
Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PA-relations) and on a major extension to include binary disjunctions of PA-relations (PA-disjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications.Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PA-relations, querying a timegraph, and efficiently checking the consistency of a timegraph augmented by a set of PA-disjunctions. Experimental results illustrate the efficiency of the proposed approach.
Computing a consistent interpretation of the variables involved in a set of temporal constraints is an important task for many areas of AI requiring temporal reasoning. We focus on the important classes of the qualitative relations in Nebel and Biirckert's ORD-Horn algebra, and of the metric constraints forming a STP, possibly augmented w i th inequations. For these tractable classes we present three new algorithms for solving the problem of finding a solution, and an efficient algorithm for determining the consistency of a STP augmented with in equations.
We consider a representation for temporal relations between intervals introduced by James Allen, and its associated computational or reasoning problem: given possibly indefinite knowledge of the rela- tions between some intervals, how do we compute the strongest possible assertions about the relations between some or all intervals. Determining exact solutions to this problem has been shown to be (almost assuredly) intractable. Allen gives an approximation algorithm based on constraint prop- agation. We giv e new approximation algorithms, examine their effectiveness, and determine under what conditions the algorithms are exact.
We present here a qualitative temporal reasoning system that takes both points and durations as primitive objects and allows relative and indefinite information. We formaly define a point duration network, as a structure formed by two point algebra (PA) networks separately but not independently, since ternary constraints are introduced for relating point and duration information. We adapt some of the concepts and reasoning techniques developed for the point algebra networks, such as consistency and minimality. We prove that the problem of determining consistency in a point duration network is NP-complete. A simpler and polynomial-time decision problem is introduced for a restricted kind of point duration networks. Finally we suggest how to determine consistency and find minimal point duration network in the general case.
In this paper we address the problem of scalability in temporal reasoning. In particular, new algorithms for efficiently managing large sets of relations in the Point Algebra are provided. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms presented in this work concern the construction of a timegraph from a given set of relations and are implemented in a temporal reasoning system called TG-II. Experimental results show that our approach is very efficient, especially when the given relations admit representation as a collection of chains connected by relatively few cross-chain links.
We are interested here in the design of a very efficient Time-Map Manager, able to deal with a large knowledge-base of several thou sand time-tokens in demanding applications such as reactive planning and execution con trol. A system, called IxTeT, aiming at that goal is described. It uses an original represen tation of a lattice of time-points that relies for efficiency on a maximum spanning tree of the lattice together with a particular indexing of its nodes. The IxTeT system is sound and complete, it has the same expressive power as the restrict ed Interval Algebra that permits complete ness in polynomial time. Its average complexi ty is shown experimentally to be linear, with a low overhead constant, for both operations: retrieval in and updating of a set of temporal relations.
Many applications|from planning and scheduling to problems in molecular biology| rely heavily on a temporal reasoning component. In this paper, we discuss the design and empirical analysis of algorithms for a temporal reasoning system based on Allen's in uential interval-based framework for representing temporal information. At the core of the system are algorithms for determining whether the temporal information is consistent, and, if so, nding one or more scenarios that are consistent with the temporal information. Two important algorithms for these tasks are a path consistency algorithm and a backtracking algorithm. For the path consistency algorithm, we develop techniques that can result in up to a ten-fold speedup over an already highly optimized implementation. For the backtracking algorithm, we develop variable and value ordering heuristics that are shown empirically to dramatically improve the performance of the algorithm. As well, we show that a previously suggested reformulation of the backtracking search problem can reduce the time and space requirements of the backtracking search. Taken together, the techniques we develop allow a temporal reasoning component tosolve problems that are of practical size. 1.
Temporal Constraint Networks are a well-defined, natural and efficient formalism for representing temporal knowledge based on metric temporal constraints. They support the representation of both metric and some qualitative temporal relations and are provided with efficient algorithms based on CSP techniques. Recently, a generalization based on fuzzy sets has been proposed in order to cope with vagueness in temporal relations. In this paper we generalize some earlier definitions for Fuzzy Temporal Constraint Networks, we identify and define interesting queries in a fuzzy temporal constraint network, an explore a method for efficiently computing them in a specific case. Further analysis of some measures on possibility distributions turns out to be fundamental in order to precisely determine some of these queries. We discuss the advantages and shortcomings of various choices and propose specific alternatives which satisfactorily avoid the problems of previous proposals. The results presented in this paper can be useful in the design of a system for temporal reasoning under uncertainty. for instance, we have applied them to defining a possibilistic temporal logic where approximate and temporal representation and reasoning are consistently combined. This work has been partially supported by Spanish MEC grant FPI-PN90 77909683 and by CICYT project ARREL (TIC92-0579-C02-01). Peer reviewed
We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiability-testing procedures. Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NP-hard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NP-hard tasks degrades rapidly with small increases in input size, something will need to be given up to obtain acceptable behavior....
It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P 6= NP ). This paper shows that NP-complete problems can be summarized by at least one "order parameter ", and that the hard problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for K-colorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability of a solution changes abruptly from near 0 to near 1. It is the high density of wellseparated almost solutions (local minima) at this boundary that cause search algorithms to "thrash". This boundary is a type of phase transition and we show that it is preserved under mappings between problems. We show that for some P problems either there is no phase transition or it occurs for bounded N (and so bound...
While the worst-case computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORD-Horn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORD-Horn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORD-Horn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm. Contents 1 Introduction 1 2 Allen's...
Path-consistency algorithms, which are polynomial for discrete problems, are exponential when applied to problems involving quantitative temporal information. The source of complexity stems from specifying relationships between pairs of time points as disjunction of intervals. We propose a polynomial algorithm, called ULT, that approximates path-consistency in Temporal Constraint Satisfaction Problems (TCSPs). We compare ULT empirically to path-consistency and directional path-consistency algorithms. When used as a preprocessing to backtracking, ULT is shown to be 10 times more effective then either DPC or PC-2. 1. Introduction Problems involving temporal constraints arise in various areas of computer science such as scheduling, circuit and program verification, parallel computation and common sense reasoning. Several formalisms for expressing and reasoning with temporal knowledge have been proposed, most notably Allen's interval algebra (Allen 83), Vilain and Kautz's point algebra (...
Reasoning about one's personal schedule of appointments is a common but surprisingly complex activity. Motivated by the novel application of planning and temporal reasoning techniques to this problem, we have extended the formalization of the temporal distance model of Dechter, Meiri, and Pearl. We have developed methods for using dates as reference intervals and for meeting the challenge of repeated activities, such as weekly recurring appointments. Introduction Intelligently managing a busy personal schedule is not an easy task, but it is a ubiquitous one. The benefit to be derived from an automated facility for maintaining an appointment calendar---with all of the complex constraint management that that entails 1 ---is potentially enormous. In the context of CLASM, 2 an intelligent appointment manager, we have begun to explore the utility of AI methods for maintaining a library of complex activity descriptions, verifying whether an activity is possible, and checking the consi...
this paper we demonstrate how metric and Allen-style constraint networks be integrated in a constraint-based reasoning system. The highlights of the work include a simple but powerful logical language for expressing both quantitative and qualitative information; translations algorithms between the metric and Allen sublanguages that entail a minimal loss of information; and a constraint-propagation procedure for problems expressed in a combination of metric and Allen constraints.
Abstract Much temporal information is qualitative information such as ‘‘The Cuban Missile crisis took place during Kennedy’s presidency,’’ where only the ordering of the end points of the two events is specified. A point and an interval algebra have been proposed for representing qualitative temporal information about the relationships between pairs of intervals and pairs of points, respectively. In this thesis, we address two fundamental reasoning tasks that arise in these algebras: Given (possibly indefinite) knowledge,of the relationships between some intervals or points, • find a scenario that is consistent with the information provided, and • find the feasible relationships between some or all pairs of intervals or points. Solutions to these tasks have applications in natural language processing, planning, plan recognition, diagnosis, and knowledge-based systems. For the task of finding consistent scenarios the main results are as follows. For the point algebra, we develop an O(n,) time, where n is the number of points, and show that a previously
Let < be a non-reflexive partial ordering defined on a set P . Let G ( P , <) be the undirected graph whose vertices are the elements of P , and whose edges ( a , b ) connect vertices for which either a < b or b < a . A graph G with vertices P for which there exists a partial ordering < such that G = G ( P , <) is called a comparability graph.
In §2 we state and prove a characterization of those graphs, finite or infinite, which are comparability graphs. Another proof of the same characterization has been given in (2), and a related question examined in (6). Our proof of the sufficiency of the characterization yields a very simple algorithm for directing all the edges of a comparability graph in such a way that the resulting graph partially orders its vertices.
This paper revises and expands upon a paper presented by two of the present authors at AAAI 1986 (Vilain & Kautz 1986). As with the original, this revised document considers computational aspects of interval- based and point-based temporal representations. Computing the consequences of temporal assertions is shown to be computationally intractable in the interval-based representation, but not in the point-based one. However, a fragment of the interval language can be expressed using the point language and benefits from the tractability of the latter. The present paper departs from the original primarily in correcting claims made there about the point algebra, and in presenting some closely related results of van Beek (1989).
An interval-based temporal logic is introduced together with a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between expressive power and the efficiency of its deductive engine. A notion of reference intervals is introduced which captures the temporal hierarchy implicit in many domains, and which can be used to precisely control the amount of deduction performed automatically by the system. Examples are provided for a database containing historical data, a database used for modeling processes and process interaction, and a database for an interactive system where the present moment is continually being updated.
This paper extends network-based methods of constraint satisfaction to include continuous variables, thus providing a framework for processing temporal constraints. In this framework, called temporal constraint satisfaction problem (TCSP), variables represent time points and temporal information is represented by a set of unary and binary constraints, each specifying a set of permitted intervals. The unique feature of this framework lies in permitting the processing of metric information, namely, assessments of time differences between events. We present algorithms for performing the following reasoning tasks: finding all feasible times that a given event can occur, finding all possible relationships between two given events, and generating one or more scenarios consistent with the information provided.
We distinguish between simple temporal problems (STPs) and general temporal problems, the former admitting at most one interval constraint on any pair of time points. We show that the STP, which subsumes the major part of Vilain and Kautz's point algebra, can be solved in polynomial time. For general TCSPs, we present a decomposition scheme that performs the three reasoning tasks considered, and introduce a variety of techniques for improving its efficiency. We also study the applicability of path consistency algorithms as preprocessing of temporal problems, demonstrate their termination and bound their complexities.
An interval order is a binary relation ≺ on a set X that is irreflexive and satisfies the condition: if x ≺ y and z ≺ w then x ≺ w or z ≺ y. An interval order is a special kind of strict partial order (transitive, irreflexive) and a generalization of the semiorder concept. If X is countable then there are real-valued functions u and p on X such that p is positive and [x ≺ y if and only if u(x) + p(x) < u(y)], if and only if ≺ is an interval order.
Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An interval-based framework and a point-based framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points.For the point-based framework and a restricted version of the interval-based framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n2)-time algorithm for finding one consistent scenario that is an O(n) improvement over the previously known algorithm, where n is the number of intervals or points, and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm. For the unrestricted version of the interval-based framework, finding a consistent scenario and finding the feasible relations have been shown to be NP-complete. We show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems.
This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the distance between time points) and qualitative, disjunctive constraints (specifying the relative position of temporal objects). Reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques, such as backtracking and path consistency. New classes of tractable problems are characterized, involving qualitative networks augmented by quantitative domain constraints, some of which can be solved in polynomial time using arc and path consistency.
A data structure called a PQ-tree is introduced. PQ-trees can be used to represent the permutations of a set U in which various subsets of U occur consecutively. Efficient algorithms are presented for manipulating PQ-trees. Algorithms using PQ-trees are then given which test for the consecutive ones property in matrices and for graph planarity. The consecutive ones test is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs. All of these algorithms require a number of steps linear in the size of their input.
The calculus of time intervals defined by Allen has been extended in various ways in order to accomodate the need for considering other time objects than convex intervals (eg.time points and intervals, non convex intervals). This paper introduces and investigates the calculus of generalized intervals, which subsumes these extensions in an algebraic setting. The set of (p,q)-relations, which generalizes the set of relations in the sense of Allen, has both an order structure and an algebraic structure. We show that, as an order, it is a distributive lattice whose properties express the topological properties of the set of (p,q)-relations. We also determine in what sense the algebraic operations of transposition and composition act continuously on this set. In Allen's algebra, the subset of relations which can be translated into conjunctive constraints on the endpoints using only <,>,=,≤,≥ has special computational significance (the constraint propagation algorithm is complete when restricted to such relations). We give a geometric characterization of a similar subset in the general case, and prove that it is stable under composition. As a consequence of this last fact, we get a very simple explicit formula for the composition of two elements in this subset.
Interval consistency problems deal with events, each of which is assumed to be an interval on the real line or on any other linearly ordered set. This paper deals with problems in reasoning about such intervals when the precise topological relationships between them is unknown or only partially specified. This work unifies notions of interval algebras for temporal reasoning in artificial intelligence with those of interval orders and interval graphs in combinatorics, obtaining new algorithmic and complexity results of interest to both disciplines. Several versions of the satisjiability, minimum labeling and all consistent solutions problems for temporal (interval) data are investigated. The satisfiability question is shown to be NP-complete even when restricting the possible interval relationships to subsets of the relations intersection and precedence only. On the other hand, we give efficient algorithm for several other restrictions of the problem. Many of these problems are also important in molecular biology, archaeology, and resolving mutual-exclusion constraints in circuit design.
This paper gives an elementary proof of the tractability of a sub-class of temporal relations in Allen's algebra and related temporal calculi, the class of preconvex relations. In Allen's case, this subclass coincides with the class of ORD-Horn relations. Nebel and Burckert defined ORD-Horn relations and proved that path-consistency is a sufficient condition for consistency of a network for this sub-class. We prove a stronger result: for each path-consistent network in the sub-class, we give an effective method for constructing a feasible scenario without backtrack.
We describe a fragment of Allen’s full algebra of time interval relations (the algebra of convex relations) that is useful for describing the dynamic behavior of technical systems. After an intuitive description of the fragment we give two formal definitions and prove that they are equivalent. This provides the basis for the major result of the paper: in a time net in which all interval relations are convex the test for the global consistency of the edge labelling can be carried out in polynomial time (in the general case it is NP-complete). This result makes convex interval relations an attractive candidate whereever qualitative reasoning about technical systems requires testing for global instead of local consistency.
. Global consistency is an important property inbinary constraint satisfaction problems. It implies minimalityin the sense that the edges contain all and only the labels thatcan participate in a global solution, which, for instance, is animportant property in querying temporal knowledge bases.Another, computational, advantage of a globally consistentnetwork is that finding a solution can be done in a backtrackfreemanner. In this paper, we propose two new subclasses ofthe interval...
We present a fast algorithm for solving qualitative interval constraint problems, which returns solutions of random problems in less than half a second on average, with the hardest problem taking only half a minute on a RISC workstation. This is a surprising result considering the problem is NP-complete. The fast solution time is attributed to the extraordinary pruning power of the path-consistency computation, and to the fact that all our randomly generated interval networks of size ⩾ 14 were found to be inconsistent, which is rapidly detected by a path-consistency computation.While inconsistency is relatively easy to prove, our algorithm also solves large consistent networks with 100 edges. We conclude that our algorithm suffices for solving qualitative interval constraint problems in practice. Other conclusions are that path-consistency reduces the solution search to an almost linear selection of atomic labels and that path-consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes.
Search is fundamental to artificial intelligence (AI) and numerous sophisticated search methods have been developed. We present a general, simple model of search processes and use it to analytically determine some typical behavior when applied to large problems. In particular, this identifies abrupt changes in overall search cost as small improvements are made in the underlying method. We also examine the robustness of this model's predictions in a range of more realistic cases. More generally, we introduce a criterion for determining when average case results reflect typical behavior which allows the method developed here to be used for investigating other large-scale behaviors of complex AI systems.
We prove a reduction theorem for prime (simple) graphs in Cunningham’s sense. Roughly speaking this theorem says that every
prime (simple) graph of ordern>5 “contains” a smaller prime graph of ordern−1. As an application we give a polynomial algorithm for recognizing circle graphs.
The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and at algorithm for finding the biconnected components of an undirect graph are presented. The space and time requirements of both algorithms are bounded by for some constants , and , where V is the number of vertices and E is the number of edges of the graph being examined.
The problem of representing temporal knowledge arises in many areas of computer science. In applications in which such knowledge is imprecise or relative, current representations based on date lines or time instants are inadequate. An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between expressive power and the efficiency of its deductive engine. A notion of reference intervals is introduced which captures the temporal hierarchy implicit in many domains, and which can be used to precisely control the amount of deduction performed automatically by the system. Examples are provided for a data base containing historical data, a data base used for modeling processes and process interaction, and a data base for an interactive system where the present moment is continually being updated.
The TIMELOGIC system is an interval-based forward-chaining inference engine and database manager of temporal constraints. Relational constraints, indicating relative order between intervals, are based on Allen's interval logic. The TIMELOGIC system also supports durational constraints, indicating relative magnitude between intervals, and reference links, used for the explicit or automatic construction of interval hierarchies. Constraints are posted and propagated in user-defined contexts with inheritance.
We analyze the problem of computing the minimal labels for a network of temporal relations in the Point Algebra. van Beek proposes an algorithm for accomplishing this task which takes time (for n points and m -relations). We show that the proof of the correctness of this algorithm given by van Beek and Cohen is faulty, and we provide a new proof showing that the algorithm is indeed correct.
According to present genetic theory, the fine structure of genes consists of linearly ordered elements. A mutant gene is obtained by alteration of some connected portion of this structure. By examining data obtained from suitable experiments, it can be determined whether or not the blemished portions of two mutant genes intersect or not, and thus intersection data for a large number of mutants can be represented as an undirected graph. If this graph is an “interval graph,” then the observed data is consistent with a linear model of the gene. The problem of determining when a graph is an interval graph is a special case of the following problem concerning (0, l)-matrices: When can the rows of such a matrix be permuted so as to make the l’s in each column appear consecutively? A complete theory is obtained for this latter problem, culminating in a decomposition theorem which leads to a rapid algorithm for deciding the question, and for constructing the desired permutation when one exists.
It is described how representation structures for counting the
number of endpoint sequences associated with a given interval order or
interval graph can be used in temporal reasoning. Efficient algorithms
for constructing such structures from temporal data are designed and
analyzed. The endpoint sequence closure problem for temporal (interval)
data is defined here as the problem of determining all possible interval
representations consistent with the given data. The results demonstrate
polynomial time solutions to several special cases of the endpoint
sequence closure problem and suggest a number of directions for further
research
In some temporal reasoning systems, inequations can give rise to disjunctions of inequations when variable elimination is performed. Motivated by this observation, we extend previous research on temporal constraints by considering disjunctions of inequations (under the assumption that time is dense.) We present results on consistency checking, canonical forms and variable elimination for this new class of temporal constraints. 1 INTRODUCTION In recent years temporal reasoning has received much attention from the artificial intelligence and database community (see [SG88, Sno90] for surveys). This is a rather natural trend since reasoning about time is essential in many applications (e.g., natural language understanding, planning, scheduling etc.). In the artificial intelligence community in particular, some researchers have introduced binary constraint networks as reasoning tools for problems involving temporal constraints [All83, VKvB89, LM88, DMP91, KL91, Mei91]. Much of this work ha...
Many applications -- from planning and scheduling to problems in molecular biology -- rely heavily on a temporal reasoning component. In this paper, we discuss the design and empirical analysis of algorithms for a temporal reasoning system based on Allen's influential interval-based framework for representing temporal information. At the core of the system are algorithms for determining whether the temporal information is consistent, and, if so, finding one or more scenarios that are consistent with the temporal information. Two important algorithms for these tasks are a path consistency algorithm and a backtracking algorithm. For the path consistency algorithm, we develop techniques that can result in up to a ten-fold speedup over an already highly optimized implementation. For the backtracking algorithm, we develop variable and value ordering heuristics that are shown empirically to dramatically improve the performance of the algorithm. As well, we show that a previously suggested reformulation of the backtracking search problem can reduce the time and space requirements of the backtracking search. Taken together, the techniques we develop allow a temporal reasoning component to solve problems that are of practical size. Comment: See http://www.jair.org/ for any accompanying files
Processing temporal constraint networks Also available as UCI technical report
- E Schwalb
- R Dechter
The role of combinatorical sructures in temporal reasoning
- A Belfer
- M Golumbic
A. Belfer & M. Golumbic. (1981). The role of combinatorical sructures in temporal reasoning. Technical report, IBM research report.