TY - GEN

T1 - Tight analysis of a collisionless robot gathering algorithm

AU - Sharma, Gokarna

AU - Busch, Costas

AU - Mukhopadhyay, Supratik

AU - Malveaux, Charles

PY - 2015/12/11

Y1 - 2015/12/11

N2 - We consider the fundamental problem of gathering a set of n robots in the Euclidean plane which have a physical extent and hence they 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 has applications in many real world scenarios including fast autonomous coverage formation. Cord-Landwehr et al. (SOFSEM 2011) gave a local greedy algorithm in a 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 paper, we improve significantly the round complexity of their algorithm to R + 2 · (n - 1) rounds. We also prove that there are initial configurations of n robots in this problem where at least R + (n - 1) over 2 rounds are needed by any local greedy algorithm. Furthermore, we improve the lower bound to R + (n - 1) rounds for the algorithm of Cord-Landwehr et al.. These results altogether provide a tight runtime analysis of their algorithm.

AB - We consider the fundamental problem of gathering a set of n robots in the Euclidean plane which have a physical extent and hence they 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 has applications in many real world scenarios including fast autonomous coverage formation. Cord-Landwehr et al. (SOFSEM 2011) gave a local greedy algorithm in a 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 paper, we improve significantly the round complexity of their algorithm to R + 2 · (n - 1) rounds. We also prove that there are initial configurations of n robots in this problem where at least R + (n - 1) over 2 rounds are needed by any local greedy algorithm. Furthermore, we improve the lower bound to R + (n - 1) rounds for the algorithm of Cord-Landwehr et al.. These results altogether provide a tight runtime analysis of their algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84958152651&partnerID=8YFLogxK

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U2 - 10.1109/IROS.2015.7354108

DO - 10.1109/IROS.2015.7354108

M3 - Conference contribution

AN - SCOPUS:84958152651

T3 - IEEE International Conference on Intelligent Robots and Systems

SP - 5189

EP - 5194

BT - IROS Hamburg 2015 - Conference Digest

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2015

Y2 - 28 September 2015 through 2 October 2015

ER -