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A Note on Two Problems in Connexion With Graphs
Abstract
We consider a graph with n vertices, all pairs of which are connected by an edge; each edge is of given positive length. The following two basic problems are solved. Problem 1: construct the tree of minimal total length between the n vertices. (A tree is a graph with one and only one path between any two vertices.) Problem 2: find the path of minimal total length between two given vertices.
... The essence of the algorithm for calculating the poles and vectors of a city graph is that for each point N of a graph G, the minimum distances from this point to all points of the graph under consideration are calculated [44,66]. The maximum value is then selected among all the minimum distances between points-as a result, the value R(N) is determined, characterizing this point in the graph G [67]. ...
... where: M r BB(X) is the minimum distance between the vertices of the graph and M r BB(i) is the maximum distance between each pair of vertices of the graph. The essence of the algorithm for calculating the poles and vectors of a city graph is that for each point N of a graph G, the minimum distances from this point to all points of the graph under consideration are calculated [44,66]. The maximum value is then selected among all the minimum distances between points-as a result, the value R(N) is determined, characterizing this point in the graph G [67]. ...
... The task of routing on the transport network is a key aspect of transport logistics. To address this, Dijkstra's algorithm [66] was utilized. For example, the calculation of the optimal route between meso-districts is as follows: 1 → 21: the optimal path [1,3,4,16,18,20,21], with a distance of 21.91 km. ...
The rapid growth of cities significantly impacts the development of transport and logistics infrastructure (TLI), creating substantial challenges for the transport network and quality of life. To enhance the efficiency and sustainability of TLI, various approaches, planning methods, and management strategies are employed at the city or agglomeration level. The objective of this study was to investigate, using graph theory and correlation analysis, the relationship between the polarity and logistic flow of the city’s meso-districts. Based on these findings, recommendations for the development of the city’s transport and logistics infrastructure were proposed. The logistic flow, influenced by social, economic, institutional, and environmental factors, plays a critical role in the planning and operation of transport and logistics infrastructure within each meso-district of the city. The determination of the polarity of meso-districts was conducted based on expert assessments by specialists, while the indicators of logistic flow were derived from the average values of statistical data for the period 2021–2023. The results demonstrated that a reduction in the polarity of meso-districts—characterized by multilateral connections between meso-districts and key indicators of logistic flows—can positively influence the quality and accessibility of the city’s transport and logistic infrastructure. This approach enables the identification of the most problematic meso-districts within the city, the mapping of logistic flow directions, and the determination of strategic development pathways for the city’s transport and logistics infrastructure (TLI). Furthermore, it was established that the polarity of the meso-district graph reflects the state of traffic congestion within the districts and its environmental impact. This correlation provides valuable insights into refining the planning and development of the city’s TLI, ensuring a more sustainable and efficient urban transport system. This study contributed to the development of the city’s transport and logistics infrastructure by proposing a comprehensive model that enhances the understanding and strengthens the interconnections between meso-districts and urban logistics. The findings hold significant implications for urban planning, as they highlight the necessity of a detailed consideration of the role of meso-districts, as well as targeted investments in transport and logistics infrastructure to ensure its sustainable development in the future.
... The Dijkstra's Algorithm, developed by Edsger W. Dijkstra in 1956, is a cornerstone in the operations research field for addressing the shortest path optimization problems. It uses a priority queue to explore the shortest path from a source vertex to all other vertices in a weighted graph [38]. The major advantage of Dijkstra's Algorithm lies in its ability to handle graphs with nonnegative weights efficiently, making it indispensable for applications in routing and navigation systems [39]. ...
... The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Table 6 Crane operational cost used as the weight for crane path planning. (1,32), (2,32), (3,32), (4,32), (5,33), (6,33), (7,34), (8,35), (9,36), (10,37), (11,38), (12,38), (13,38), (14,38), (15,38), (16,38), (17,38), (18,38), (19,38), (20,38), (21,38), (22,38), (23,38), (24,38), (25,38), (26,38), (27,38), (28,38), (29,38), (30,38), (31,39), (32,39), (33,40), (34,41), (35,41), (36,41), (37,41), (38,41), (39,41), ( ...
... The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Table 6 Crane operational cost used as the weight for crane path planning. (1,32), (2,32), (3,32), (4,32), (5,33), (6,33), (7,34), (8,35), (9,36), (10,37), (11,38), (12,38), (13,38), (14,38), (15,38), (16,38), (17,38), (18,38), (19,38), (20,38), (21,38), (22,38), (23,38), (24,38), (25,38), (26,38), (27,38), (28,38), (29,38), (30,38), (31,39), (32,39), (33,40), (34,41), (35,41), (36,41), (37,41), (38,41), (39,41), ( ...
Designing temporary crane transit paths in large construction sites with varying geological profiles presents two challenges: (1) ensuring safe, efficient, and cost-effective operations, and (2) developing optimization solutions that consider material properties, ground loading, and site layout. This paper addresses these challenges by integrating a graph search algorithm with crane mat structural design to optimize crane mat layouts and transit paths. A case study of structural steel subassembly installations, based on a real-world project, demonstrates the method’s effectiveness. The results highlight safety-focused crane mat designs and transit plans, along with significant cost savings compared to traditional heuristics.
... This limitation necessitates the use of weighted graph search algorithms to meet UAV-specific requirements. For weighted graphs, several sophisticated algorithms have been developed, including the well-known Dijkstra's algorithm [57]. Dijkstra's algorithm, a greedy approach, guarantees an optimal path from the start to the goal, provided such a path exists. ...
... In the learning phase, as shown in Figure 10a, PRM constructs a roadmap by randomly sampling nodes (light blue dots) in the configuration space and connecting neighboring nodes that are obstacle-free (black line segments). During the querying phase, as depicted in Figure 10b, PRM performs a graph search (such as Dijkstra [57] or A* [59]) on this roadmap to find a collision-free path from the start to the goal (red line segments). Compared to searching-based approaches, PRM lowers memory usage and computational demands. ...
Unmanned aerial vehicles (UAVs) are widely employed across diverse fields due to their flexibility and scalability. However, achieving full autonomy remains a challenge as human intervention is still required in most scenarios. Motion planning, a cornerstone of UAV autonomous navigation, has garnered extensive attention, with numerous advanced algorithms having been proposed in recent years. This paper provides a comprehensive overview of UAV motion planning frameworks, systematically addressing three key components: map representation, path planning, and trajectory optimization. Map representation establishes environmental awareness, path planning balances efficiency and safety in path generation, and trajectory optimization refines paths into feasible, energy-efficient motions. Unlike prior reviews focused on specific techniques, this study offers an integrated perspective, helping researchers understand the overall framework and recent advancements in UAV motion planning. Additionally, emerging trends and potential strategies are discussed to improve the efficiency, adaptability, and robustness of UAVs to meet increasingly complex mission requirements.
... This means that we can apply pathfinding algorithms. Dijkstra's algorithm [Dij22] when applied to this graph, amounts to a form of brute-force search where we iterate over the sets of errors in order of increasing cost until we reach a valid decoding END ∈ EXIT which is an early stop to the traditional Dijkstra's algorithm. Tesseract is able to go much faster than this by exploiting the A* pathfinding algorithm [HNR68], as explained below. ...
Tesseract is a Most-Likely Error decoder designed for low-density-parity-check quantum error-correcting codes. Tesseract conducts a search through a graph on the set of all subsets of errors to find the lowest cost subset of errors consistent with the input syndrome. Although this graph is exponentially large, the search can be made efficient in practice for random errors using search technique along with a few pruning heuristics. We show through benchmark circuits for surface, color, and bivariate-bicycle codes that Tesseract is significantly faster than integer programming-based decoders while retaining comparable accuracy at moderate physical error rates. We also find that Tesseract can decode transversal CNOT protocols for surface codes on neutral atom quantum computers. Finally, we compare surface code and bivariate bicycle code circuits, finding that the [[144,12,12]] bivariate bicycle code is to more efficient than surface codes using our most-likely error decoding, whereas using correlated matching and BP+OSD decoders would have implied only a improvement. Assuming instead that long-range couplers are noisier, the improvement drops to around using Tesseract or using correlated matching and BP+OSD.
... If the distance parameter is missing, then it behaves like the classic p-median approach where the objective is to minimize traveling costs. To solve this problem, first, an origin-destination (OD) cost matrix is created using Dijkstra's shortest path algorithm (Dijkstra, 1959) and edited using Hillsman calibration method. Then, a group of good semi-random solutions is created to feed a metaheuristic for further optimization. ...
Location-allocation is a widely used approach to optimally select earthquake shelters and efficiently allocate the population in case of an emergency. A significant limitation often ignored by the vast majority of studies is the utilization of static aggregations of residential population, which may lead to sub-optimal location decisions and inefficient allocations. To overcome this limitation, in this article, an attempt to spatially refine population data, as well as, to capture population fluctuations throughout the day, using areal interpolation methods along with open spatial information, is undertaken. Then, its influence on the shelter location selection and population allocation process is examined. The city of Mytilini, Lesvos, Greece is used as the case study to further investigate three location-allocation scenarios using block-level census population, building-level night and day estimations as input. The results indicate that using spatially refined population data provide reduced distances, better shelter selection and capacity optimization, and finally, more efficient allocations. Moreover, using building-level day estimations of the population distribution reveals significant shifts in sheltering demand from residential areas to mixed and commercial zones. The use of detailed population dynamics data can give insights about the adequacy of shelter provision under different scenarios, and therefore, help civil protection authorities to make much more informed decisions.
... However, realtime execution is typically not required in global planning. Nonetheless, the size of the map can present challenges for slower algorithms such as Dijkstra's shortest path [30]. Consequently, heuristics are often employed to reduce execution time. ...
Autonomous driving research has gained attention in recent years due to its great potential in reshaping transportation systems. It is highly noticeable that most research focuses on well-maintained urban roads, whereas much less effort is pushed for low or unstructured scenarios usually found in suburban or countryside areas of emerging countries. This study systematically reviews state-of-the-art trajectory planning for car-like vehicles in these environments.We analyzed 4601 papers published in the last 10 years and selected 75 studies. Based on the selected research, we summarize the techniques for global planning, local planning, motion control, and multi-vehicle collaborative planning. In particular, we highlight the strengths and weaknesses of the local planning approaches and discuss and identify common limitations, such as sensor faults, terrain variations, safety and regulatory risks. Moreover, we summarize the most adopted visual input sensors, their associated data structures that are used as search spaces for local planning, and sensor fusion techniques, which complement the advantages of different types of sensors. Furthermore, we provide a systematic schema that relates the dependencies between the visual sensors, data-representations, and local planning techniques. From this, we identify gaps in the current literature, suggesting possible directions for future work.
... The shortest path of a node is the path with minimal cost and the average of the shortest paths from 205 that node to any other node in the network. It was calculated using Dijkstra's algorithm (Dijkstra, 1959). ...
Background: The brain operates through networks of interconnected regions, which can be disrupted by glial tumors and their treatment. This study investigates associations between thisaltered functional network topology and cognition in gliomas.
Methods: We studied 50 adult glioma survivors (>1-year post-therapy) and 50 healthy controls. Participants underwent cognitive assessments across six domains and an 8-minute resting-state functional MRI. Based on the BOLD signal, partial correlations were computed among 78 brain regions. From their absolute values, whole-brain and nodal graph metrics were derived and normalized to random graphs. Group differences in whole-brain and nodal graph metrics were assessed with Mann-Whitney U tests and mixed-design ANOVAs respectively. Metrics exhibiting significant intergroup differences were correlated with cognitive scores, with pbonf<.050 indicating significance.
Results: Among controls, 8/78 nodes were identified as hubs. Patients exhibited significantly higher whole-brain clustering, correlating with intelligence (r(98)=-.409,pbonf<.001) and executive functioning (r(98)=.300, pbonf=.014). Lower centrality, higher nodal clustering and assortativity were also observed in patients, particularly in hubs, correlating with language and executive functioning, respectively (all r(98)>.300, pbonf<.050).
Conclusion: Glioma patients commonly experience cognitive deficits alongside post-treatment alterations in functional network topology. Alterations in clustering, assortativity and centralitymay specifically act as compensatory mechanisms, significantly influencing cognitive function.
... By using this information to map out the area, the fastest route to a specific destination can be determined. Path-planning algorithms, such as A* [39], Dijkstra's algorithm [41], and APF, are commonly used in scenarios such as maze navigation and autonomous vehicles. These algorithms enable real-time decision-making for the robot, ensuring it reaches its goal quickly while avoiding collisions [42]. ...
The integration of Autonomous Mobile Robots (AMRs) in various industrial and service settings has increased, driving significant demand for enhanced performance and control capabilities. These robots face challenges in achieving high-speed navigation and precise maneuvering in dynamic environments filled with both mobile and stationary obstacles. Conventional controllers often fall short in these scenarios, necessitating innovative solutions.
This thesis aims to address these challenges by developing a path planning and tracking module for wheeled ground mobile robots that incorporate obstacle avoidance capabilities. The primary objective is to advance the development of controllers that enable robots to navigate safely, quickly, and accurately in dynamic environments.
First, a comprehensive literature review is performed to examine existing work on mobile robot controllers, trajectory definition, and obstacle avoidance strategies. This review is supplemented with essential background information on these topics. Next, for trajectory tracking, a Nonlinear Model Predictive Control (NMPC) is implemented to control an omnidirectional robot. As for collision avoidance, two methods are proposed: one using virtual security zones to halt the robot, and another using online spline generation for obstacle avoidance.
The results for trajectory tracking are derived from both simulations and experiments with real robots. The controller is implemented within the widely adopted Robot Operating System (ROS) framework, with simulations conducted in the Gazebo simulator. Moreover, comparisons between different state-of-the-art controllers are also presented. For collision avoidance, results are obtained from simulations performed in Matlab. The obstacle avoidance algorithm is tested against various obstacle configurations and shapes.
Overall, the proposed trajectory tracking controller improves precision in both position and orientation without significantly increasing processing time, based on simulations and real-world experiments. As for collision avoidance, the obstacle avoidance algorithm successfully generates smooth trajectories across several obstacle configurations, ensuring safe navigation around obstacles.
... Schematic of the porous structures and their Radical tessellation for cases with (a) low porosity, (b) high porosity, (c) background particles structure, and (d) background particle method, which considers both the actual particles and the background particles.After obtaining all possible diffusion paths (the edges) in the porous packing structure, Dijkstra's path search algorithm is employed to find all possible paths from the starting point to the end point[60,61]. ...
Estimating the tortuosity of porous electrodes is important for understanding the performance of lithium-ion batteries and optimizing the design of electrode microstructures. In this work, a new method for estimating the tortuosity of porous electrodes is proposed based on radical tessellation, and the results agree well with those calculated by empirical formulas and finite element simulations. Compared with empirical formulas, the proposed method can estimate tortuosity for more complicated microstructures, regardless of particle distribution and size dispersity; compared with finite element simulations, the proposed method offers a significant advantage in computational efficiency. Based on the method, the influence of different microstructure characters on the tortuosity is discussed. It is found that in addition to the porosity, the particle size and particle aggregation morphology are all critical in influencing the tortuosity of the porous electrode. Finally, the tortuosity obtained by this method is integrated into the Pseudo-2-dimensional (P2D) model for the calculation of effective properties, and the results show that this method offers an efficient way in improving the prediction accuracy of P2D models.
... The two most well-known methods for solving the eikonal equation are the fast marching [107,122] and the fast sweeping [143,142] methods. They are both finite difference-based schemes that trace back to Dijkstra's algorithm [50]. Both methods require specialized data structures that present a barrier to their integration into many of the high-order finite element codes used by the scientific computing community. ...
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge--Amp\`ere equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. In this paper, we describe the LVPP algorithm in a general form and apply it to twelve problems from across mathematics.
... In general, one can simply assume that there are N edges connecting each pair with haziness values, some of which may be 8. In the context of IsUMap, the Dijkstra algorithm [8] is then applied to compute the distance function d Γ on the resulting global graph Γ. ...
Many machine learning algorithms try to visualize high dimensional metric data in 2D in such a way that the essential geometric and topological features of the data are highlighted. In this paper, we introduce a framework for aggregating dissimilarity functions that arise from locally adjusting a metric through density-aware normalization, as employed in the IsUMap method. We formalize these approaches as m-schemes, a class of methods closely related to t-norms and t-conorms in probabilistic metrics, as well as to composition laws in information theory. These m-schemes provide a flexible and theoretically grounded approach to refining distance-based embeddings.
... Given both the SD-WAN and SDN cell-free controllers use software to optimise the routing of the transmissions up to the cloud data centre, different routing algorithms can be used to control the path these transmissions take. Within this work, we compare two different routing algorithms: Shortest Path Maximum Bandwidth (SPMB) [17], being an extension of Dijkstra's shortest path algorithm [52], and Minimum Cost Flow Routing (MCFR) [22], based on a multi-source and multi-target extension the minimum cost flow problem [53], and their impact on network delay within the cell-free architecture. ...
To the best of our knowledge, we offer the first IoT-Osmotic simulator supporting 6G and Cloud infrastructures, leveraging the similarities in Software-Defined Wide Area Network (SD-WAN) architectures when used in Osmotic architectures and User-Centric Cell-Free mMIMO (massive multiple-input multiple-output) architectures. Our simulator acts as a simulator orchestrator, supporting the interaction with a patient digital twin generating patient healthcare data (vital signs and emergency alerts) and a VANET simulator (SUMO), both leading to IoT data streams towards the cloud through pre-initiated MQTT protocols. This contextualises our approach within the healthcare domain while showcas-ing the possibility of orchestrating different simulators at the same time. The combined provision of these two aspects, joined with the addition of a ring network connecting all the first-mile edge nodes (i.e., access points), enables the definition of new packet routing algorithms, streamlining previous solutions from SD-WAN architectures, thus showing the benefit of 6G architectures in achieving better network load balancing, as well as showcasing the limitations of previous approaches. The simulated 6G architecture, combined with the optimal routing algorithm and MEL (MICROELEMENTS software components) allocation policy, was able to reduce the time required to route all communications from IoT devices to the cloud by upto 50.4% compared to analogous routing algorithms used within 5G architectures.
... Both experimental areas are based on road data from the OSM (OpenStreetMap) platform, with 20 randomly selected delivery points for couriers (indicated by yellow circles in the figures). The shortest paths are calculated using the Dijkstra algorithm [50], and a cost matrix is constructed as the data basis for algorithm testing. Experimental Area 1 covers 4.6487 km 2 , with 772 road nodes and 1088 road segments, as shown in Figure 7. Experimental Area 2 covers 9.4326 km 2 , with 1364 road nodes and 2236 road segments, as shown in Figure 8. ...
The Traveling Salesman Problem (TSP) is a classical discrete combinatorial optimization problem that is widely applied in various domains, including robotics, transportation, networking, etc. Although existing studies have provided extensive discussions of the TSP, the issues of improving convergence and optimization capability are still open. In this study, we aim to address this issue by proposing a new algorithm named IDINFO (Improved version of the discretized INFO). The proposed IDINFO is an extension of the INFO (weighted mean of vectors) algorithm in discrete space with optimized searching strategies. It applies the multi-strategy search and a threshold-based 2-opt and 3-opt local search to improve the local searching ability and avoid the issue of local optima of the discretized INFO. We use the TSPLIB library to estimate the performance of the IDINFO for the TSP. Our algorithm outperforms the existing representative algorithms (e.g., PSM, GWO, DSMO, DJAYA, AGA, CNO_PSO, Neural-3-OPT, and LIH) when tested against multiple benchmark sets. Its effectiveness was also verified in the real world in solving the TSP in short-distance delivery.
... is the shortest path between the node pair (v τ i , v τ j ) computed by the Dijkstra algorithm [87]. ...
Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.
We provide a mathematical framework for identifying the shortest path in a maze using a Grover walk, which becomes non-unitary by introducing absorbing holes. In this study, we define the maze as a network with vertices connected by unweighted edges. Our analysis of the stationary state of the truncated Grover walk on finite graphs, where we strategically place absorbing holes and self-loops on specific vertices, demonstrates that this approach can effectively solve mazes. By setting arbitrary start and goal vertices in the underlying graph, we obtain the following long-time results: (i) in tree structures, the probability amplitude is concentrated exclusively along the shortest path between start and goal; (ii) in ladder-like structures with additional paths, the probability amplitude is maximized near the shortest path.
This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold (DM)-ROM methodology is computationally efficient, avoids pixelation or interpolation of flow field data, and is adaptable to various grids and geometries. The framework consists of four main steps: First, a convolutional neural network-based parameterization network extracts nonlinear shape modes directly from aerodynamic geometries. Next, manifold learning is applied to reduce the dimensionality of the high-fidelity output flow fields. A multilayer perceptron-based regression network is then trained to map the nonlinear input and output modes. Finally, a back-mapping process reconstructs the full flow field from the predicted low-dimensional output modes. DM-ROM is rigorously tested on a transonic RAE2822 airfoil test case, which includes shock waves of varying strengths and locations. Metrics are introduced to quantify the model's accuracy in predicting shock wave strength and location. The results demonstrate that DM-ROM achieves a field prediction error of approximately 3.5% and significantly outperforms reference ROM techniques, such as proper orthogonal decomposition (POD)-ROM and isometric mapping (ISOMAP)-ROM, for various training sample sizes.
A number of different types of information are generally associated with places. It is estimated that about 75-90% of information may contain an official link to a specific area, expressed as, for example, coordinates, or addresses, and therefore has a spatial character, making data collection a responsible and important stage, which reasonably affects the quality of its results. Information and its sources are treated with particular care and rigor in the scientific field: in most cases, the data must be relevant, reliable, technically simple, and collected quickly at reasonable costs. The analysis of geographic information makes it possible to obtain qualitatively new information and reveal previously unknown patterns. Modern data collection methods are divided into three distinct groups: terrestrial, cartographic, and remote. Remote or aerospace methods are considered to be those that allow information to be collected. It refers to objects on the Earth's surface, phenomena, or processes from space or the atmosphere, recorded by detecting electromagnetic radiation on the ground across various spectral ranges. The involvement of various platforms (providers) of surveillance equipment makes it possible to divide them into: space, aerial photography, and images from Unmanned Aerial Vehicles (UAVs). As a technology justified on security grounds, UAVs show great promise in many areas of application. Effective planning of drone missions allows for the collection of larger sets of data with a higher level of detail and in a shorter period of time. The continuity of information collection for a given territory allows for the most accurate and reliable three-dimensional modelling, spatial analysis and geostatistics of the local situation.
Private mobility electrification is slowed down by technical limitations, such as the low autonomy of electric vehicles (EVs) compared to internal combustion engine vehicles (ICEVs). As a consequence, accurate planning of the route is needed before a travel with an EV begins. Routing algorithms are of crucial importance to identify the route which allows to minimize total travel time, reducing the drawbacks of battery's limited energy density. The complexity of the problem and the size of road networks considered for this task imply computational times which are not in line with users' needs. The method proposed in this paper employs clustering and pruning techniques to speed up planning by downsizing the network analyzed during route planning. By reducing the computational cost, it is possible to apply Dijkstra algorithm, which provides an exact minimization of total travel time.
Hot spots policing involves the targeted deployment of police patrols to areas where high levels of crime have previously been observed. For hot spots policing to be effective, it requires analysis of crime data to identify the specific locations where crime is concentrated and the creation of suitable patrol routes. The creation of hot spots policing patrol routes is a manual task that police officers perform, requiring skills and knowledge about hot spots policing and crime pattern analysis for the patrols to be effective in reducing crime. These requirements can limit the use of hot spots policing where these skills and knowledge are not available, and where they are available, the creation of patrol routes can be a time-consuming task. In this paper, we introduce two computational route generation heuristics that automate the creation of hot spots policing patrol routes. Both approaches identify the specific locations where crime concentrates and then use different methods to create the patrol routes. We compare the performance of each approach using metrics associated with effective patrol route creation and through visual inspection. We conclude that the heuristics we introduce provide an accurate means for creating hot spots policing patrol routes, which can support greater and improved use of hot spot policing as an effective type of intervention for decreasing crime.
The core control of a haircutting robot lies in the motion planning and execution of its manipulator arm. As a mechanical system with high degrees of freedom, each hair-cutting action requires precise control algorithms to ensure smoothness and accuracy of movement. This section focuses on the algorithmic modeling of haircutting actions, covering inverse kinematics, neural network–based control strategies, and other intelligent control methods to ensure the robot’s flexibility and safety during the haircutting process.
With the rapid development of global retail e-commerce, the critical role of warehouses in logistics systems has become increasingly prominent. Current state-of-the-art solutions typically address only one or two warehouse tasks, including object recognition, sorting, and transportation. This paper presents the development of an integrated autonomous warehouse robot system capable of performing the three functions. The system mimics human capabilities by integrating various components, including advanced computer vision technologies using YOLOv5, a mobile robot, and a robotic arm. The YOLOv5 algorithm is employed for object detection and size estimation, enabling the system to classify goods-containing boxes into small, medium, and large categories. These classified goods are then delivered to predetermined locations by the mobile robot. Finally, the robot arm is employed to pick and place boxes in their storage location based on size. Experimental results demonstrate the system’s robustness and reliability, highlighting its significant potential to enhance warehouse management through roboticautomation.
Code generation and understanding are critical capabilities for large language models (LLMs). Thus, most LLMs are pretrained and fine-tuned on code data. However, these datasets typically treat code as static strings and rarely exploit the dynamic information about their execution. Building upon previous work on trace modeling, we study Execution Tuning (E.T.), a training procedure in which we explicitly model real-world program execution traces without requiring manual test annotations. We train and evaluate models on different execution trace granularities (line and instruction-level) and strategies on the task of output prediction, obtaining around 80% accuracy on CruxEval and MBPP, and showing the advantages of dynamic scratchpads (i.e., self-contained intermediate computations updated by the model rather than accumulated as a history of past computations) on long executions (up to 14k steps). Finally, we discuss E.T.'s practical applications.
Lunar-rover path planning is a key topic in lunar exploration research, with safety and computational efficiency critical for achieving long-distance planning. This paper proposes a distributed path-planning method that considers multiple lunar environmental factors, addressing the issues of inadequate safety considerations and low computational efficiency in current research. First, a set of safety evaluation rules is constructed by considering factors such as terrain slope, roughness, illumination, and rock abundance. Second, a distributed path-planning strategy based on a safety-map tile pyramid (DPPS-STP) is proposed, using a weighted A* algorithm with hash table-based open and closed lists (OC-WHT-A*) on a Spark cluster for efficient and safer path planning. Additionally, high-resolution digital orthophoto maps (DOM) are utilized for small crater detection, enabling more refined path planning built upon the overall mission-planning result. The method was validated in four lunar regions with distinct characteristics. The results show that DPPS-STP, which considers multiple environmental factors, effectively reduces the number of hazardous nodes and avoids crater obstacles. For long-distance tasks, it achieves an average speedup of up to 11.5 times compared to the single-machine OC-WHT-A*, significantly improving computational efficiency.
Orchard robots play a crucial role in agricultural production. Autonomous navigation serves as the foundation for orchard robots and eco-unmanned farms. Accurate sensing and localization are prerequisites for achieving autonomous navigation. However, current vision-based navigation solutions are sensitive to environmental factors, such as light, weather, and background, which can affect positioning accuracy. Therefore, they are unsuitable for outdoor navigation applications. LIDAR provides accurate distance measurements and is suitable for a wide range of environments. Its immunity to interference is not affected by light, colour, weather, or other factors, making it suitable for low objects and complex orchard scenes. Therefore, LiDAR navigation is more suitable for orchard environments. In complex orchard environments, tree branches and foliage can cause Global Positioning System (GNSS) accuracy to degrade, resulting in signal loss. Therefore, the major challenge that needs to be addressed is generating navigation paths and locating the position of orchard robots. In this paper, an improved method for Simultaneous Localization and Mapping (SLAM) and A-star algorithm is proposed. The SLAM and path planning method designed in this study effectively solves the problems of insufficient smoothness and large curvature fluctuation of the path planned in the complex orchard environment, and improves the detection efficiency of the robot. The experimental results indicate that the method can consistently and accurately fulfil the robot's detection needs in intricate orchard environments.
Simultaneous localization and mapping (SLAM) is one of the key technologies for agricultural robots to build maps and localize in complex orchard environments and realize unmanned autonomous operations. Due to the complexity of the orchard environment, the single canopy feature and the diffuse reflection of light caused by the leaves, etc., the map construction process of the orchard environment leads to mismatch and increases the cumulative error of the map construction. Aiming at the above problems, this paper propose a navigation map construction method for orchard environment based on the fusion of Scan Context and NDT-ICP. The method firstly searches the Ring key quickly to get the candidate frames, and scores the similarity between the candidate frames and the current frame, and effectively detects the loopbacks by two-stage searching algorithm to reduce the false matches in the map of orchard environment. Meanwhile, a point cloud alignment method based on the fusion of normal distribution transform coarse alignment and iterative nearest point exact alignment is used to reduce the cumulative error of the orchard environment map. The results show that the improved algorithm compensates the drift of the point cloud map with higher mapping accuracy, better real-time performance, lower resource utilization, higher overlap between the trajectory estimation and the real trajectory, smoother loops, and a 4% reduction in CPU occupancy. In the complex orchard environment, the root mean square error and standard deviation of the trajectories of this paper's algorithm are 0.57 m and 0.19 m, which are 68% and 83% higher than those of the loop detection algorithms in the Lightweight Ground Optimized Lidar Trajectory Measurement and Multivariate Terrain Mapping (LeGO-LOAM), respectively. Accurate map construction and low drift pose estimation can be performed.The research algorithm effectively reduces the influence of mis-matching and large cumulative error in the process of map construction in the orchard environment, meets the demand for high-precision environmental mapping in the orchard environment, and provides technical support for promoting unmanned operation in the orchard environment.
The precessing vortex core (PVC) oscillation is a commonly observed self-excited flow instability associated with the precession of the vortex breakdown bubble around the flow axis in swirl flows. The flow region where internal feedback forcing sustains the PVC is called the wavemaker. Linear stability analysis (LSA) methods, in conjunction with large-eddy simulation (LES), can be used to identify a wavemaker. Here, we assess a data-driven approach using complex network analysis (CNA) to identify the wavemaker of a nominally axisymmetric turbulent swirl nozzle flow using unsteady data from a prior LES for which wavemaker predictions from LSA are available. Networks are constructed using time-resolved velocity data from the LES. Internodal connectivity is defined using either correlation or mutual information, and weighted closeness centrality is used to identify network hubs in each case. These hubs identify the wavemaker when mapped back to physical space. Both networks predict the position of the wavemaker in good agreement with the prior LSA result, with the mutual information network providing a closer match to the wavemaker’s spatial extent. These results show that CNA can be applied reliably to extract wavemaker information from time-series data of turbulent swirl flow.
Shortest path problem in a network is a fundamental task in combinatorial optimization. Many applications in practice involve optimization two conflicting criteria and from a biobjective shortest path problems. Since there does not exist a single solution that is optimal with respect to both objective functions, we are interested in a special set of solutions for which any of the two criteria cannot be improved without declining the other: Pareto optimal set or Pareto front. In this paper we analyze in details the biobjective shortest path problem in the case in which the first objective function is a linear one (minimal length paths) and the second one is a nonlinear bottleneck function (maximal capacity paths). We present an exact solution based on two modifications of the Dijkstra’s algorithm that finds the complete description of all Pareto optimal solutions. We provide detailed poofs of the correctness and the computational complexity of the presented algorithms and numerical examples that illustrate their execution.
Weinberger: Formal Procedures, for Connecting Terminals with a Minimum Total Wire Length
- H Loberman
- H. Loberman