Local strategies for maintaining a chain of relay stations between an explorer and a base station

Dynia, Miroslaw; Kutyłowski, Jarosław; Heide, Friedhelm Meyer auf der; Schrieb, Jonas

doi:10.1145/1248377.1248420

Cited by 16 publications

(7 citation statements)

References 15 publications

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“…Kutyłowski [13] gives a lower bound of Ω n 2 − εn . A seemingly better strategy, called CHASE-EX-PLORER, has been suggested by Dynia et al [9]. It considers a variant of the communication chain problem where one of the base stations (the explorer) is mobile.…”

Section: Known Results and Our Contributionmentioning

confidence: 99%

Convergence of local communication chain strategies via linear transformations

Kling

Heide

2011

Proceedings of the Twenty-Third Annual ACM Symposium on Parallelism in Algorithms and Architectures

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Consider two far apart base stations connected by an arbitrarily winding chain of n relay robots to transfer messages between them. Each relay acts autonomously, has a limited communication range, and knows only a small, local part of its environment. We seek a strategy for the relays to minimize the chain's length. We describe a large strategy class in form of linear transformations of the spatial vectors connecting neighboring robots. This yields surprising correlations between several strategy properties and characteristics of these transformations (e.g., "reasonable" strategies correspond to transformations given by doubly stochastic matrices). Based on these results, we give almost tight bounds on the strategies' convergence speed by applying and extending results about the mixing time of Markov chains. Eventually, our framework enables us to define strategies where each relay bases its decision where to move only on the positions of its k next left and right neighbors, and to prove a convergence speed of Θ n 2 k 2 log n for these strategies. This not only closes a gap between upper and lower runtime bounds of a known strategy (GO-TO-THE-MIDDLE), but also allows for a trade-off between convergence properties and locality.

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Section: Known Results and Our Contributionmentioning

confidence: 99%

Convergence of local communication chain strategies via linear transformations

Kling

Heide

2011

Proceedings of the Twenty-Third Annual ACM Symposium on Parallelism in Algorithms and Architectures

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“…In this context, disoriented robots (no agreement on the local coordinate systems) that are connected in a chain topology are assumed as well as a circular connectivity range and viewing range of 1. We prove that the GTM algorithm [6,13], in which each robot moves to the midpoint between its two direct neighbors in every round, converges to the optimal configuration in O(n 2 •log(n/ε)) epochs assuming the Ssync scheduler. For one-dimensional configurations (all robots are initially collinear) this is a significant improvement over the so far best known runtime bound of O(n 5 • log(n/ε)) epochs for this algorithm [6].…”

Section: Our Contributionmentioning

confidence: 99%

“…Later on, an almost matching lower bound (for the algorithm) of Ω(n 2 • log(1/ε)) has been derived [16]. Algorithms with stronger assumptions, e.g., the LUMI model, are able to achieve better runtimes [13,17].…”

Section: Related Workmentioning

confidence: 99%

The Max-Line-Formation Problem

Castenow¹,

Götte²,

Knollmann³

et al. 2021

Preprint

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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 together (e.g., Gathering or Chain-Formation). In this work, we introduce the Max-Line-Formation problem, which has a contrary goal: to arrange the robots on a straight line of maximal length.First, we prove that the problem is impossible to solve by robots with a constant sized circular viewing range. The impossibility holds under comparably strong assumptions: robots that agree on both axes of their local coordinate systems in Fsync. On the positive side, we show that the problem is solvable by robots with a constant square viewing range, i.e., the robots can observe other robots that lie within a constant-sized square centered at their position. In this case, the robots need to agree on only one axis of their local coordinate systems. We derive two algorithms: the first algorithm considers oblivious robots (OBLOT ) and converges to the optimal configuration in time O(n 2 • log(n/ε)) under the Ssync scheduler (ε is a convergence parameter). The other algorithm makes use of locally visible lights (LUMI). It is designed for the Fsync scheduler and can solve the problem exactly in optimal time Θ(n). We also argue how a combination of the two algorithms can solve the Max-Line-Formation exactly in time O(n 2 ) under the Ssync scheduler with the help of the LUMI model.Afterward, we show that both the algorithmic and the analysis techniques can also be applied to the Gathering and Chain-Formation problem: we introduce an algorithm with a reduced viewing range for Gathering and give new and improved runtime bounds for the Chain-Formation problem.

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“…Existing approaches to create AMRoNet are mostly based on mobile routers making a chain. In [4,13] the authors present different strategies such as Manhattan-Hopper, Hopper, Chase explorer and Go-to-The-Middle for maintaining the connectivity of an explorer with a base station. In [20], depending on whether the knowledge of the agent's trajectory is available or not, the trajectories for the routers are estimated.…”

Section: Related Workmentioning

confidence: 99%

Deployment of Mobile Routers Ensuring Coverage and Connectivity

Mathews

Mathew

2012

IJCNC

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Maintaining connectivity among a group of autonomous agents exploring an area is very important, as it promotes cooperation between the agents and also helps message exchanges which are very critical for their mission. Creating an underlying Ad-hoc Mobile Router Network (AMRoNet) using simple robotic routers is an approach that facilitates communication between the agents without restricting their movements. We address the following question in our paper: How to create an AMRoNet with local information and with minimum number of routers? We propose two new localized and distributed algorithms 1) agent-assisted router deployment and 2) a self-spreading for creating AMRoNet. The algorithms use a greedy deployment strategy for deploying routers effectively into the area maximizing coverage and a triangular deployment strategy to connect different connected component of routers from different base stations. Empirical analysis shows that the proposed algorithms are the two best localized approaches to create AMRoNets.

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Local strategies for maintaining a chain of relay stations between an explorer and a base station

Cited by 16 publications

References 15 publications

Convergence of local communication chain strategies via linear transformations

Convergence of local communication chain strategies via linear transformations

The Max-Line-Formation Problem

Deployment of Mobile Routers Ensuring Coverage and Connectivity

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