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 ALGOSENSORS 2021 (accepted)
TI - Gathering a Euclidean Closed Chain of Robots in Linear Time
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
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 - 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 - 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 - 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 - 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
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 - 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 - 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 - 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 - 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 - 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 -
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 -