Friedhelm Meyer auf der Heide

• Prof. Dr.
• Professor at Paderborn University

Consider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the server cloud scheduling problem, in which the jobs have to be processed either on a single local machine or on one of infinitel...

In this paper, we survey recent results regarding the Gathering problem in the research area of distributed computing by mobile robots. We assume a simple, standard model of robots: they are point-shaped, live in a d- dimensional Euclidean space, are disoriented (do not agree on common directions or orientations), and have limited visibility (can o...

We consider a scenario where a server is wirelessly connected to countless sensor nodes that continuously measure data. The task of the server is to monitor the sensors’ data. More precisely, at each time step the server calculates a function defined over the current measurements of the sensors. Since the sensors only have small computational power...

We consider formation problems for chains of disoriented, mobile robots with limited visibility operating in asynchronous rounds (Async). More precisely, we study the Chain-Formation and the Gathering problem. Chain-Formation considers a chain of robots between two stationary outer robots: Each inner robot has two identifiable neighbors, and the go...

We consider a swarm of $n$ robots in a $d$-dimensional Euclidean space. The robots are oblivious (no persistent memory), disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering requires that all robots reach the same, not predefined position....

The famous $k$-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively. However, to the best of our knowledge, no research has considered the problem if the servers are not identical and requests can express which servers should serve them. Therefore, we present a new model generalizing th...

Most existing robot formation problems seek a target formation of a certain minimal and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to reach a maximal structure, supporting, for example, an efficient coverage in exploration scenarios. As a first step...

We examine the Online Facility Location problem in an extended version. Fotakis showed a lower bound of Ω(log⁡nlog⁡log⁡n) for the original Online Facility Location problem, where n is the number of clients. This bound holds even on the real line and for randomized algorithms against oblivious adversaries. We propose randomized online algorithms in...

We consider n robots with limited visibility: each robot can observe other robots only up to a constant distance denoted as the viewing range. The robots operate in discrete rounds that are either fully synchronous (\(\mathcal {F}\textsc {sync}\)) or semi-synchronized (\(\mathcal {S}\textsc {sync}\)). Most previously studied formation problems in t...

Product Creation (PC) refers to the process of planning and developing a product as well as related services from the initial idea until manufacturing and distribution. Throughout this process, there are numerous tasks that depend on human expertise and are typically undertaken by experienced practitioners. As the field of Artificial Intelligence (...

We focus on the following question about Gathering of n autonomous, mobile robots in the Euclidean plane: Is it possible to solve Gathering of robots that do not agree on their coordinate systems (disoriented) and see other robots only up to a constant distance (limited visibility) in linear time? Up to now, such a result is only known for robots o...

We consider n robots with limited visibility: each robot can observe other robots only up to a constant distance denoted as the viewing range. The robots operate in discrete rounds that are either fully synchronous (FSync) or semi-synchronized (SSync). Most previously studied formation problems in this setting seek to bring the robots closer togeth...

Consider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the Server Cloud Scheduling problem, in which the jobs have to be processed either on a single local machine or on one of many clou...

We extend the Mobile Server problem introduced in Feldkord and Meyer auf der Heide (TOPC 6(3), 14:1–14:17 2019) to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. To reduce communication costs, the positions of the servers can be adapted by a limited distance ms per round f...

In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile robots with limited viewing range in the plane. Remarquably, this algorithm exploits the fact that during its execution, many collisions of robots occur. Such collisions are interprete...

Consider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the Server Cloud Scheduling problem, in which the jobs have to be processed either on a single local machine or on one of many clou...

The complexity of development and deployment in today’s IT world is enormous. Despite the existence of so many pre-fabricated components, frameworks, cloud providers, etc., building IT systems still remains a major challenge and most likely overtaxes even a single ambitious developer. This results in spreading such development and deployment tasks...

This work focuses on the following question related to the Gathering problem of n autonomous, mobile robots in the Euclidean plane: Is it possible to solve Gathering of disoriented robots with limited visibility in \(o(n^2)\) fully synchronous rounds ( Open image in new window )? The best known algorithm considering the \(\mathcal {OBLOT}\) model (...

Most existing robot formation problems seek a target formation of a certain minimal and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to reach a maximal structure, supporting for example an efficient coverage in exploration scenarios. A recent example i...

Over the past decades, the Gathering problem, which asks to gather a group of robots in finite time given some restrictions, has been intensively studied. In this paper, we are given a group of n autonomous, dimensionless, deterministic, and anonymous robots, with bounded viewing range. Assuming a continuous time model, the goal is to gather these...

This work focuses on the following question related to the Gathering problem of $n$ autonomous, mobile robots in the Euclidean plane: Is it possible to solve Gathering of robots that do not agree on any axis of their coordinate systems (disoriented robots) and see other robots only up to a constant distance (limited visibility) in $o(n^2)$ fully sy...

Most existing robot formation problems seek a target formation of a certain \emph{minimal} and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to reach a \emph{maximal} structure, supporting for example an efficient coverage in exploration scenarios. A re...

In this work, we initiate the research about the Gathering problem for robots with limited viewing range in the three-dimensional Euclidean space. In the Gathering problem, a set of initially scattered robots is required to gather at the same position. The robots’ capabilities are very restricted – they do not agree on any coordinate system or comp...

We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set $S$ of commodities. Ravi and Sinha (SODA'04) introduced the model as the Multi-Commodity Facility Location Problem (MFLP) and considered it an offline optimization problem. The model itself...

In this work, we initiate the research about the Gathering problem for robots with limited viewing range in the three-dimensional Euclidean space. In the Gathering problem, a set of initially scattered robots is required to gather at the same position. The robots' capabilities are very restricted -- they do not agree on any coordinate system or com...

We consider a swarm of n autonomous mobile robots distributed on a 2-dimensional grid. A basic task for such a swarm is to perform the gathering process: All robots have to gather at one not predefined place. On the grid there are configurations which, due to symmetry, cannot be gathered at a single point. Such configurations are 2×2 squares. There...

We extend the Mobile Server Problem introduced in [8] to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. In order to reduce communication costs, the positions of the servers can be adapted by a limited distance \(m_s\) per round for each server. The costs are measured simil...

Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing of operations of different families. A job is completed when its latest operation completes and the goal is to...

In this paper, we present the first algorithm for progressive sampling of 3D surfaces with blue noise characteristics that runs entirely on the GPU. The performance of our algorithm is comparable to state‐of‐the‐art GPU Poisson‐disk sampling methods, while additionally producing ordered sequences of samples where every prefix exhibits good blue noi...

Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing of operations of different families. A job is completed when its latest operation completes and the goal is to...

We introduce the Mobile Server problem, inspired by current trends to move computational tasks from cloud structures to multiple devices close to the end user. An example of this is embedded systems in autonomous cars that communicate to coordinate their actions. Our model is a variant of the classical Page Migration problem. More formally, we cons...

We extend the Mobile Server Problem, introduced in SPAA'17, to a model where k identical mobile resources, here named servers, answer requests appearing at points in the Euclidean space. In order to reduce communication costs, the positions of the servers can be adapted by a limited distance m_s per round for each server. The costs are measured sim...

We present a peer-to-peer network that supports the efficient processing of orthogonal range queries Open image in new window in a d-dimensional point space. The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG’07). We show how to execute such range queries using \(\mathc...

We present a technique for rendering highly complex 3D scenes in real-time by generating uniformly distributed points on the scene's visible surfaces. The technique is applicable to a wide range of scene types, like scenes directly based on complex and detailed CAD data consisting of billions of polygons (in contrast to scenes handcrafted solely fo...

We introduce the mobile server problem, inspired by current trends to move computational tasks from cloud structures to multiple devices close to the end user. An example for this are embedded systems in autonomous cars that communicate in order to coordinate their actions. Our model is a variant of the classical Page Migration Problem. More formal...

We consider simple models of swarms of identical, anonymous robots: they are points in the plane and “see” only their neighbors (robots within distance one). We will deal with distributed local protocols of such swarms that result in formations like “gathering at one point”. The focus will be on protocols assuming a continuous time model. We presen...

We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The corresponding graph theoretic problem seeks a strongly connected dominating-absorbent set of minimum cardinality in...

We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive onl...

Consider a scheduling problem in which a set of tasks needs to be scheduled on m parallel processors. Each task (Formula presented.) consists of a set of jobs with interjob communication demands, represented by a weighted, undirected graph (Formula presented.). The processors are assumed to be interconnected by a shared communication channel, which...

A parameterized problem is fixed-parameter parallelizable (FPP) if it can be solved in O(f(k)⋅(log⁡N)α) time using O(g(k)⋅Nβ) processors, where N is the input size, k is the parameter, f and g are arbitrary computable functions, and α, β are constants independent of N and k. We re-examine the k-vertex cover problem from a parameterized parallel com...

We consider a scenario where agents have to exchange data in a wireless ad-hoc network, although it is not connected. We assume that each agent has a static home base. To improve connectivity, each agent is allowed to move away from his home base, but only for a limited distance which may be different for different agents. These distances might be...

We examine the Online Facility Location Problem in an augmented version, where the online algorithm is allowed to adapt the position of the facilities for costs proportional to the distance by which the position is changed. In this setting, it is possible to construct online algorithms which deal with the lower bound instances of Online Facility Lo...

Consider a problem in which n jobs that are classified into k types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time. The machine requires a setup taking s time units whenever it switches from processing jobs of one type to jobs of a different type. We consider the problem a...

We consider the scenario of n sensor nodes observing streams of data. The nodes are connected to a central server whose task it is to compute some function over all data items observed by the nodes. In our case, there exists a total order on the data items observed by the nodes. Our goal is to compute the k currently lowest observed values or a val...

We consider online leasing problems in which demands arrive over time and need to be served by leasing resources. We introduce a new model for these problems in which a resource can be leased for K different durations each incurring a different cost (longer leases cost less per time unit). Each demand i can be served any time between its arrival \(...

We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement Open image in new window. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of \(r_j\), it is processed at an x-fractio...

We consider continuous strategies for swarms of robots in the Euclidean plane. In such a strategy, each robot continuously observes its local neighborhood, and continuously adapts speed and direction following a local rule. We present two main results. The first defines a class of strategies, the contracting strategies, that perform gathering in ti...

We consider a swarm of n autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are...

Consider a network in which n distributed nodes are connected to a single server. Each node continuously observes a data stream consisting of one value per discrete time step. The server has to continuously monitor a given parameter defined over all information available at the distributed nodes. That is, in any time step t, it has to compute an ou...

We consider the scenario of $n$ sensor nodes observing streams of data. The nodes are connected to a central server whose task it is to compute some function over all data items observed by the nodes. In our case, there exists a total order on the data items observed by the nodes. Our goal is to compute the $k$ currently lowest observed values or a...

Consider a problem in which $n$ jobs that are classified into $k$ types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time. The machine requires a setup taking $s$ time units whenever it switches from processing jobs of one type to jobs of a different type. We consider the pro...

We introduce the mobile server problem, inspired by current trends to move computational tasks from cloud structures to multiple devices close to the end user. An example for this are embedded systems in autonomous cars that communicate in order to coordinate their actions. Our model is a variant of the classical Page Migration Problem. More formal...

Consider a network in which $n$ distributed nodes are connected to a single server. Each node continuously observes a data stream consisting of one value per discrete time step. The server has to continuously monitor a given parameter defined over all information available at the distributed nodes. That is, in any time step $t$, it has to compute a...

Many graph problems such as maximum cut, chromatic number, hamiltonian cycle, and edge dominating set are known to be fixed-parameter tractable (FPT) when parameterized by the treewidth of the input graphs, but become W-hard with respect to the clique-width parameter. Recently, Gajarský et al. proposed a new parameter called modular-width using the...

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: all robots have to gather at one (not predefined) place. The work in this paper is motivated by the following insight: On one side, for swarms of robots distributed in the 2-dimensional Euclidean space, s...

In this work, we reconsider the well-known Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering in the plane n autonomous mobile robots with limited viewing range. The above authors have introduced it as a discrete, round-based algorithm and proved its correctness. In [8], by Degener et al. it is shown that the algorithm...

Consider a scheduling problem in which a set of jobs with interjob communication, canonically represented by a weighted tree, needs to be scheduled on m parallel processors interconnected by a shared communication channel. In each time step, we may allow any processed job to use a certain capacity of the channel in order to satisfy (parts of) its c...

Efficiently parallelizable parameterized problems have been classified as being either in the class FPP (fixed-parameter parallelizable) or the class PNC (parameterized analog of NC), which contains FPP as a subclass. In this paper, we propose a more restrictive class of parallelizable parameterized problems called fixed-parameter parallel-tractabl...

Defining, measuring, and comparing the quality and efficiency of rendering algorithms in computer graphics is a demanding challenge: quality measures are often application specific and efficiency is strongly influenced by properties of the rendered scene and the used hardware. We survey the currently employed evaluation methods for the development...

We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive onl...

We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive onl...

We present an efficient parallel algorithm for the general Monotone Circuit Value Problem (MCVP) with n gates and an underlying graph of bounded genus k. Our algorithm generalizes a recent result by Limaye et al. who showed that MCVP with toroidal embedding (genus 1) is in NC when the input contains a toroidal embedding of the circuit. In addition...

In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate...

In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate...

Consider the continuous distributed monitoring model in which $n$ distributed nodes, receiving individual data streams, are connected to a designated server. The server is asked to continuously monitor a function defined over the values observed across all streams while minimizing the communication. We study a variant in which the server is equippe...

We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of $n$ indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid and must keep this connectivity during the whole process of their gathering. Connectivity means, that neighborin...

We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The corresponding graph theoretic problem seeks a strongly connected dominating-absorbent set of minimum cardinality in...

We consider online leasing problems in which demands arrive over time and need to be served by leasing resources. We introduce a new model for these problems such that a resource can be leased for $K$ different durations each incurring a different cost (longer leases cost less per time unit). Each demand $i$ can be served anytime between its arriva...

Many markets have seen a shift from the idea of buying and moved to leasing instead. Arguably, the latter has been the major catalyst for their success. Ten years ago, research realized this shift and initiated the study of 'online leasing problems' by introducing leasing to online optimization problems. Resources required to provide a service in a...

We consider online optimization problems in which certain goods have to be acquired in order to provide a service or infrastructure. Classically, decisions for such problems are considered as final: one buys the goods. However, in many real world applications, there is a shift away from the idea of buying goods. Instead, leasing is often a more fle...

We study a scenario in which n mobile robots with a limited viewing range are distributed in the Euclidean plane and have to solve a formation problem. The formation problems we consider are the Gathering problem and the Chain-Formation problem. In the Gathering problem, the robots have to gather in one (not predefined) point, while in the Chain-Fo...

We consider the k-token dissemination problem, where k initially arbitrarily distributed tokens have to be disseminated to all nodes in a dynamic network (as introduced by Kuhn et al., STOC 2010). In contrast to general dynamic networks, our dynamic networks are unit disk graphs, i.e., nodes are embedded into the Euclidean plane and two nodes are c...

We study two-party communication in the context of directed dynamic networks that are controlled by an adaptive adversary. This adversary is able to change all edges as long as the networks stay strongly-connected in each round. In this work, we establish a relation between counting the total number of nodes in the network and the problem of exchan...

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that...

In the gathering problem, n autonomous robots have to meet on a single point. We consider the gathering of a closed chain of point-shaped, anonymous robots on a grid. The robots only have local knowledge about a constant number of neighboring robots along the chain in both directions. Actions are performed in the fully synchronous time model FSYNC....

In the leasing variant of Set Cover presented by Anthony et al. [1], elements \(U\) arrive over time and must be covered by sets from a family \(F\) of subsets of \(U\). Each set can be leased for \(K\) different periods of time. Let \(\left| U \right| = n\) and \(\left| F \right| = m\). Leasing a set \(S\) for a period \(k\) incurs a cost \(c_{S}^...

We consider a scenario of n identical autonomous robots on a 2D grid. They are memoryless and do not communicate. Their initial configuration does not have to be connected. Each robot r knows its position p_r \in \mathbf)Z)^2. In addition, each robot knows the connected pattern F to be formed. F may be given by a set of n points in \mathbf{Z}^2, or...

Dominating set based virtual backbones are used for rou-ting in wireless ad-hoc networks. Such backbones receive and transmit messages from/to every node in the network. Existing distributed algorithms only consider undirected graphs, which model symmetric networks with uniform transmission ranges. We are particularly interested in the well-establi...

Consider n nodes connected to a single coordinator. Each node receives an individual online data stream of numbers and, at any point in time, the coordinator has to know the k nodes currently observing the largest values, for a given k between 1 and n. We design and analyze an algorithm that solves this problem while bounding the amount of messages...

In this paper we introduce 'On-The-Fly Computing', our vision of future IT services that will be provided by assembling modular software components available on world-wide markets. After suitable components have been found, they are automatically integrated, configured and brought to execution in an On-The-Fly Compute Center. We envision that these...

Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price \alpha > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from $v$ to all other n...

We study a scenario in which n nodes of a mobile ad-hoc network continuously collect data. Their task is to repeatedly update aggregated information about the data, e.g., the maximum, the sum, or the full information about all data received by all nodes at a given time step. This aggregated information has to be disseminated to all nodes. We propos...

In this survey article, we discuss two algorithmic research areas that emerge from problems that arise when resources are offered in the cloud. The first area, online leasing, captures problems arising from the fact that resources in the cloud are not bought, but leased by cloud vendors. The second area, Distributed Storage Systems, deals with prob...

We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement rj∈[0,1]. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of r_j, it is processed at an x-fraction of the full speed....

Ich habe diesen Sommer mein Abi gemacht und möchte zum Herbst mit dem Studium beginnen – Informatik natürlich! Da es in meinem kleinen Ort keine Uni gibt, werde ich deshalb in Kürze umziehen müssen. Dann heißt es, all die tausend Sachen in meinen Schränken und Regalen in Umzugskartons zu verpacken. Um den Umzug möglichst kostengünstig zu gestalten,...

We consider the \(k\)-token dissemination problem, where \(k\) initially arbitrarily distributed tokens have to be disseminated to all nodes in a dynamic network (as introduced by Kuhn et al. STOC 2010). In contrast to general dynamic networks, our dynamic networks are unit disk graphs, i.e., nodes are embedded into the Euclidean plane and two node...