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Tight Analysis of a Collisionless Robot Gathering Algorithm

Tight Analysis of a Collisionless Robot Gathering Algorithm Tight Analysis of a Collisionless Robot Gathering Algorithm GOKARNA SHARMA, Kent State University COSTAS BUSCH, SUPRATIK MUKHOPADHYAY, and CHARLES MALVEAUX, Louisiana State University We consider the fundamental problem of gathering a set of n robots in the Euclidean plane that have a physical extent and hence cannot share their positions with other robots. The objective is to determine a minimum time schedule to gather the robots as close together as possible around a predefined gathering point avoiding collisions. This problem with minimum time objective has applications in many real-world scenarios including fast autonomous coverage formation. Cord-Landwehr et al. (in Proceedings of the International Conference on Current Trends in Theory and Practice of Computer Science, 2011) gave a local greedy algorithm in a fully synchronous setting and proved that, for the discrete version of the problem where robots' movements are restricted to the positions on an integral grid, their algorithm solves this problem in O(nR) rounds, where R is the distance from the farthest initial robot position to the gathering point. In this article, we improve significantly the round complexity of their algorithm to R + 2 · (n - 1) rounds. This round complexity is obtained in the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Autonomous and Adaptive Systems (TAAS) Association for Computing Machinery

Tight Analysis of a Collisionless Robot Gathering Algorithm

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2017 by ACM Inc.
ISSN
1556-4665
DOI
10.1145/3056460
Publisher site
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Abstract

Tight Analysis of a Collisionless Robot Gathering Algorithm GOKARNA SHARMA, Kent State University COSTAS BUSCH, SUPRATIK MUKHOPADHYAY, and CHARLES MALVEAUX, Louisiana State University We consider the fundamental problem of gathering a set of n robots in the Euclidean plane that have a physical extent and hence cannot share their positions with other robots. The objective is to determine a minimum time schedule to gather the robots as close together as possible around a predefined gathering point avoiding collisions. This problem with minimum time objective has applications in many real-world scenarios including fast autonomous coverage formation. Cord-Landwehr et al. (in Proceedings of the International Conference on Current Trends in Theory and Practice of Computer Science, 2011) gave a local greedy algorithm in a fully synchronous setting and proved that, for the discrete version of the problem where robots' movements are restricted to the positions on an integral grid, their algorithm solves this problem in O(nR) rounds, where R is the distance from the farthest initial robot position to the gathering point. In this article, we improve significantly the round complexity of their algorithm to R + 2 · (n - 1) rounds. This round complexity is obtained in the

Journal

ACM Transactions on Autonomous and Adaptive Systems (TAAS) – Association for Computing Machinery

Published: Apr 11, 2017

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