Optimal strategies for maintaining a chain of relays between an explorer and a base camp

Kutyłowski, Jarosław; Heide, Friedhelm Meyer auf der

doi:10.1016/j.tcs.2008.04.010

Cited by 40 publications

(22 citation statements)

References 5 publications

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“…The first shown runtime bound was O(n 2 log(n)) [DKLH06]. Later, this has been improved [KM09]: In the Euclidean plane, the Hopper strategy delivers a √ 2-approximation of the shortest communication chain in time O(n). Restricted to a grid, the Manhattan Hopper strategy delivers an optimal solution in time O(n).…”

Section: Related Workmentioning

confidence: 99%

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Asymptotically Optimal Gathering on a Grid

Cord-Landwehr

Fischer

Jung

et al. 2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

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In this paper, we solve the local gathering problem of a swarm of n indistinguishable, pointshaped robots on a two dimensional grid in asymptotically optimal time O(n) in the fully synchronous FSYN C 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 × 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 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 robotwhich 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 O(n 2 ) [DKL + 11].

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Section: Related Workmentioning

confidence: 99%

“…One of these are the strategies for shortening communication chains, we introduced above. I.e., [DKLH06] that needs time O(n 2 log(n)) and [KM09] that needs time O(n) in the Euclidean plane as well as on a grid.…”

Section: Related Workmentioning

confidence: 99%

Asymptotically Optimal Gathering on a Grid

Cord-Landwehr

Fischer

Jung

et al. 2016

Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures

Self Cite

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“…A similar problem is considered by Kutylowski et. al [14]. They presented a global strategy for using a chain of robots to create a communication bridge between a stationary camp and a mobile explorer.…”

Section: A Related Workmentioning

confidence: 99%

Maintaining connectivity in environments with obstacles

Tekdas

Plonski

Karnad

et al. 2010

2010 IEEE International Conference on Robotics and Automation

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Robotic routers (mobile robots with wireless communication capabilities) can create an adaptive wireless network and provide communication services for mobile users ondemand. Robotic routers are especially appealing for applications in which there is a single mobile user whose connectivity to a base station must be maintained in an environment that is large compared to the wireless range.In this paper, we study the problem of computing motion strategies for robotic routers in such scenarios, as well as the minimum number of robotic routers necessary to enact our motion strategies. Assuming that the routers are as fast as the user, we present an optimal solution for cases where the environment is a simply-connected polygon, a constant factor approximation for cases where the environment has a single obstacle, and an O(h) approximation for cases where the environment has h circular obstacles. The O(h) approximation also holds for cases where the environment has h arbitrary polygonal obstacles, provided they satisfy certain geometric constraints -e.g. when the set of their minimum bounding circles is disjoint.

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“…In [4], upper bounds of O(n 2 ) for the easier convergence problem in several time models are shown, but with robots having a global view. There are algorithms with local view and runtime statements for similar problems, such as transforming a long winding chain of robots into a short one [14,9,6]. There is also work for gathering on graphs instead of Euclidean spaces [7,13,15].…”

Section: Related Workmentioning

confidence: 99%

A local O(n ² ) gathering algorithm

Degener

Kempkes

Heide

2010

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

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The gathering problem, where n autonomous robots with restricted capabilities are required to meet in a single point of the plane, is widely studied. We consider the case that robots are limited to see only robots within a bounded vicinity and present an algorithm achieving gathering in O(n 2 ) rounds in expectation. A round consists of a movement of all robots, in random order. All previous algorithms with a proven time bound assume global view on the configuration of all robots.

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Optimal strategies for maintaining a chain of relays between an explorer and a base camp

Cited by 40 publications

References 5 publications

Asymptotically Optimal Gathering on a Grid

Asymptotically Optimal Gathering on a Grid

Maintaining connectivity in environments with obstacles

A local O(n ² ) gathering algorithm

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Optimal strategies for maintaining a chain of relays between an explorer and a base camp

Cited by 40 publications

References 5 publications

Asymptotically Optimal Gathering on a Grid

Asymptotically Optimal Gathering on a Grid

Maintaining connectivity in environments with obstacles

A local O(n 2 ) gathering algorithm

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A local O(n ² ) gathering algorithm