TY - JOUR AU - Castenow, Jannik AU - Harbig, Jonas AU - Jung, Daniel AU - Knollmann, Till AU - Meyer auf der Heide, Friedhelm ID - 33947 JF - Theoretical Computer Science KW - General Computer Science KW - Theoretical Computer Science SN - 0304-3975 TI - Gathering a Euclidean Closed Chain of Robots in Linear Time and Improved Algorithms for Chain-Formation VL - 939 ER - TY - CONF AU - Castenow, Jannik AU - Harbig, Jonas AU - Jung, Daniel AU - Kling, Peter AU - Knollmann, Till AU - Meyer auf der Heide, Friedhelm ED - Hillel, Eshcar ED - Palmieri, Roberto ED - Riviére, Etienne ID - 34008 SN - 1868-8969 T2 - Proceedings of the 26th International Conference on Principles of Distributed Systems (OPODIS) TI - A Unifying Approach to Efficient (Near-)Gathering of Disoriented Robots with Limited Visibility VL - 253 ER - TY - CONF AU - Castenow, Jannik AU - Harbig, Jonas AU - Jung, Daniel AU - Knollmann, Till AU - Meyer auf der Heide, Friedhelm ED - Gasieniec, Leszek ED - Klasing, Ralf ED - Radzik, Tomasz ID - 23730 T2 - Proceedings of the 17th International Symposium on Algorithms and Experiments for Wireless Sensor Networks (ALGOSENSORS) TI - Gathering a Euclidean Closed Chain of Robots in Linear Time VL - 12961 ER - TY - CONF AU - Castenow, Jannik AU - Harbig, Jonas AU - Jung, Daniel AU - Knollmann, Till AU - Meyer auf der Heide, Friedhelm ED - Devismes, Stéphane ED - Mittal, Neeraj ID - 20185 SN - 978-3-030-64347-8 T2 - Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings TI - Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility VL - 12514 ER - TY - JOUR AU - Castenow, Jannik AU - Fischer, Matthias AU - Harbig, Jonas AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16299 JF - Theoretical Computer Science SN - 0304-3975 TI - Gathering Anonymous, Oblivious Robots on a Grid VL - 815 ER - TY - CONF AB - Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion. In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work. AU - Jung, Daniel AU - Kolb, Christina AU - Scheideler, Christian AU - Sundermeier, Jannik ID - 4563 KW - greedy routing KW - ad hoc networks KW - convex hulls KW - c-competitiveness T2 - Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS) TI - Competitive Routing in Hybrid Communication Networks ER - TY - CONF AU - Jung, Daniel AU - Kolb, Christina AU - Scheideler, Christian AU - Sundermeier, Jannik ID - 4565 SN - 9781450357999 T2 - Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA) TI - Brief Announcement: Competitive Routing in Hybrid Communication Networks ER - TY - THES AB - My dissertation deals with the Gathering problem for swarms of n point-shaped robots on a grid, in which all robots of the swarm are supposed to gather at a previously undefined point. Special attention is paid to the strong limitation of robot capabilities. These include in particular the lack of global control, a global compass, global visibility and (global) communication skills. Furthermore, all robots are identical. The robots are given only local abilities. This includes a constant range of vision. The robots all work completely synchronously. In this work we present and analyze three different Gathering strategies in different robot models. We formally prove correctness and total running time: Chapter 4 focuses on minimizing the available robot capabilities. The underlying strategy completes the gathering in O(n^2) time. For the following Chapters 5 and 6, the aim is to optimize the total running time under using only local robot capabilities: We additionally allow a constant-sized memory and a constant number of locally visible statuses (lights, flags). For the strategies of both chapters we show an asymptotically optimal running time of O(n). Unlike in Chapters 4 and 5, we additionally restrict connectivity and vision to an initially given chain connectivity in Chapter 6, where two chain neighbors must have a distance of 1 from each other. A robot can only see and interact with a constant number of its direct chain neighbors. AU - Jung, Daniel ID - 1209 SN - 978-3-942647-99-1 TI - Local Strategies for Swarm Formations on a Grid ER - TY - GEN AB - 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 autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved. AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 17811 T2 - arXiv:1702.03400 TI - Gathering Anonymous, Oblivious Robots on a Grid ER - TY - CONF AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ED - Fernández Anta, Antonio ED - Jurdzinski, Tomasz ED - Mosteiro, Miguel A. ED - Zhang, Yanyong ID - 16347 T2 - Algorithms for Sensor Systems - 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, {ALGOSENSORS} TI - Gathering Anonymous, Oblivious Robots on a Grid VL - 10718 ER - TY - GEN AB - 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 all robots within a $2\times 2$-sized area that is not known beforehand. Two robots are connected if they are vertical or horizontal neighbors on the grid. The locality constraint means that no global control, no compass, no global communication and only local vision is available; hence, a robot can only see its grid neighbors up to a constant $L_1$-distance, which also limits its movements. A robot can move to one of its eight neighboring grid cells and if two or more robots move to the same location they are \emph{merged} to be only one robot. The locality constraint is the significant challenging issue here, since robot movements must not harm the (only globally checkable) swarm connectivity. For solving the gathering problem, we provide a synchronous algorithm -- executed by every robot -- which ensures that robots merge without breaking the swarm connectivity. In our model, robots can obtain a special state, which marks such a robot to be performing specific connectivity preserving movements in order to allow later merge operations of the swarm. Compared to the grid, for gathering in the Euclidean plane for the same robot and time model the best known upper bound is $\mathcal{O}(n^2)$. AU - Cord-Landwehr, Andreas AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16450 T2 - arXiv:1602.03303 TI - Asymptotically Optimal Gathering on a Grid ER - TY - CONF AB - 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 O(n) in the fully synchronous FSYNC time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate all robots within a 2x2- sized area that is not known beforehand. Two robots are connected if they are vertical or horizontal neighbors on the grid. The locality constraint means that no global control, no compass, no global communication and only local vision is available; hence, a robot can only see its grid neighbors up to a constant L1-distance, which also limits its movements. A robot can move to one of its eight neighboring grid cells and if two or more robots move to the same location they are merged to be only one robot. The locality constraint is the significant challenging issue here, since robot move- ments must not harm the (only globally checkable) swarm connectivity. For solving the gathering problem, we provide a synchronous algorithm { executed by every robot { which ensures that robots merge without breaking the swarm con- nectivity. In our model, robots can obtain a special state, which marks such a robot to be performing specific connec- tivity preserving movements in order to allow later merge operations of the swarm. Compared to the grid, for gath- ering in the Euclidean plane for the same robot and time model the best known upper bound is O(n^2). AU - Cord-Landwehr, Andreas AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16359 T2 - Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) TI - Asymptotically Optimal Gathering on a Grid ER - TY - CONF AB - 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 neighboring robots of the chain need to be positioned at the same or neighboring points of the grid. In our model, gathering means to keep shortening the chain until the robots are located inside a 2*2 subgrid. Our model is completely local (no global control, no global coordinates, no compass, no global communication or vision, ...). Each robot can only see its next constant number of left and right neighbors on the chain. This fixed constant is called the viewing path length. All its operations and detections are restricted to this constant number of robots. Other robots, even if located at neighboring or the same grid point cannot be detected. Only based on the relative positions of its detectable chain neighbors, a robot can decide to obtain a certain state. Based on this state and their local knowledge, the robots do local modifications to the chain by moving to neighboring grid points without breaking the chain. These modifications are performed without the knowledge whether they lead to a global progress or not. We assume the fully synchronous FSYNC model. For this problem, we present a gathering algorithm which needs linear time. This result generalizes a result, where an open chain with specified distinguishable (and fixed) endpoints is considered. AU - Abshoff, Sebastian AU - Cord-Landwehr, Andreas AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16360 T2 - Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS) TI - Gathering a Closed Chain of Robots on a Grid ER - TY - GEN AB - 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 neighboring robots of the chain need to be positioned at the same or neighboring points of the grid. In our model, gathering means to keep shortening the chain until the robots are located inside a $2\times 2$ subgrid. Our model is completely local (no global control, no global coordinates, no compass, no global communication or vision, \ldots). Each robot can only see its next constant number of left and right neighbors on the chain. This fixed constant is called the \emph{viewing path length}. All its operations and detections are restricted to this constant number of robots. Other robots, even if located at neighboring or the same grid point cannot be detected. Only based on the relative positions of its detectable chain neighbors, a robot can decide to obtain a certain state. Based on this state and their local knowledge, the robots do local modifications to the chain by moving to neighboring grid points without breaking the chain. These modifications are performed without the knowledge whether they lead to a global progress or not. We assume the fully synchronous $\mathcal{FSYNC}$ model. For this problem, we present a gathering algorithm which needs linear time. This result generalizes the result from \cite{hopper}, where an open chain with specified distinguishable (and fixed) endpoints is considered. AU - Abshoff, Sebastian AU - Cord-Landwehr, Andreas AU - Fischer, Matthias AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16449 T2 - arXiv:1510.05454 TI - Gathering a Closed Chain of Robots on a Grid ER - TY - GEN AB - 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. Every robot has a limited memory that may contain one timestamp of the global clock, also visible to its direct neighbors. In this synchronous time model, there is no limited view gathering algorithm known to perform better than in quadratic runtime. The configurations that show the quadratic lower bound are closed chains. In this paper, we present the first sub-quadratic---in fact linear time---gathering algorithm for closed chains on a grid. AU - Abshoff, Sebastian AU - Andreas Cord-Landwehr, Andreas AU - Jung, Daniel AU - Meyer auf der Heide, Friedhelm ID - 16397 T2 - ArXiv: 1501.04877 TI - Towards Gathering Robots with Limited View in Linear Time: The Closed Chain Case ER - TY - CONF AB - Today's networks, like the Internet, do not consist of one but a mixture of several interconnected networks. Each has individual qualities and hence the performance of a network node results from the networks' interplay.We introduce a new game theoretic model capturing the interplay between a high-speed backbone network and a low-speed general purpose network. In our model, n nodes are connected by a static network and each node can decide individually to become a gateway node. A gateway node pays a fixed price for its connection to the high-speed network, but can utilize the high-speed network to gain communication distance 0 to all other gateways. Communication distances in the low-speed network are given by the hop distances. The effective communication distance between any two nodes then is given by the shortest path, which is possibly improved by using gateways as shortcuts.Every node v has the objective to minimize its communication costs, given by the sum (SUM-game) or maximum (MAX-game) of the effective communication distances from v to all other nodes plus a fixed price \alpha > 0, if it decides to be a gateway. For both games and different ranges of \alpha, we study the existence of equilibria, the price of anarchy, and convergence properties of best-response dynamics. AU - Abshoff, Sebastian AU - Cord-Landwehr, Andreas AU - Jung, Daniel AU - Skopalik, Alexander ED - Lavi, Ron ID - 452 T2 - Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT) TI - Brief Announcement: A Model for Multilevel Network Games ER - TY - CONF AB - We consider a multilevel network game, where nodes can improvetheir communication costs by connecting to a high-speed network.The n nodes are connected by a static network and each node can decideindividually to become a gateway to the high-speed network. The goalof a node v is to minimize its private costs, i.e., the sum (SUM-game) ormaximum (MAX-game) of communication distances from v to all othernodes plus a fixed price α > 0 if it decides to be a gateway. Between gatewaysthe communication distance is 0, and gateways also improve othernodes’ distances by behaving as shortcuts. For the SUM-game, we showthat for α ≤ n − 1, the price of anarchy is Θ (n/√α) and in this rangeequilibria always exist. In range α ∈ (n−1, n(n−1)) the price of anarchyis Θ(√α), and for α ≥ n(n − 1) it is constant. For the MAX-game, weshow that the price of anarchy is either Θ (1 + n/√α), for α ≥ 1, orelse 1. Given a graph with girth of at least 4α, equilibria always exist.Concerning the dynamics, both games are not potential games. For theSUM-game, we even show that it is not weakly acyclic. AU - Abshoff, Sebastian AU - Cord-Landwehr, Andreas AU - Jung, Daniel AU - Skopalik, Alexander ID - 395 T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE) TI - Multilevel Network Games ER -