TY - GEN

T1 - Optimal patrolling of fragmented boundaries

AU - Collins, Andrew

AU - Czyzowicz, Jurek

AU - Ga̧sieniec, Leszek

AU - Kosowski, Adrian

AU - Kranakis, Evangelos

AU - Krizanc, Danny

AU - Martin, Russell

AU - Ponce, Oscar Morales

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - A set of mobile robots is deployed on a simple curve of finite length, composed of a finite set of vital segments separated by neutral segments. The robots have to patrol the vital segments by perpetually moving on the curve, without exceeding their uniform maximum speeds. The quality of patrolling is measured by the idleness, i.e., the longest time period during which any vital point on the curve is not visited by any robot. Given a configuration of vital segments, our goal is to provide algorithms describing the movement of the robots along the curve so as to minimize the idleness. Our main contribution is a proof that the optimal solution to the patrolling problem is attained either by the cyclic strategy, in which all the robots move in one direction around the curve, or by the partition strategy, in which the curve is partitioned into sections which are patrolled separately by individual robots. These two fundamental types of strategies were studied in the past in the robotics community in different theoretical and experimental settings. However, to our knowledge, this is the first theoretical analysis proving optimality in such a general scenario. Throughout the paper we assume that all robots have the same maximum speed. In fact, the claim is known to be invalid when this assumption does not hold, cf. [Czyzowicz et al., Proc. ESA 2011].

AB - A set of mobile robots is deployed on a simple curve of finite length, composed of a finite set of vital segments separated by neutral segments. The robots have to patrol the vital segments by perpetually moving on the curve, without exceeding their uniform maximum speeds. The quality of patrolling is measured by the idleness, i.e., the longest time period during which any vital point on the curve is not visited by any robot. Given a configuration of vital segments, our goal is to provide algorithms describing the movement of the robots along the curve so as to minimize the idleness. Our main contribution is a proof that the optimal solution to the patrolling problem is attained either by the cyclic strategy, in which all the robots move in one direction around the curve, or by the partition strategy, in which the curve is partitioned into sections which are patrolled separately by individual robots. These two fundamental types of strategies were studied in the past in the robotics community in different theoretical and experimental settings. However, to our knowledge, this is the first theoretical analysis proving optimality in such a general scenario. Throughout the paper we assume that all robots have the same maximum speed. In fact, the claim is known to be invalid when this assumption does not hold, cf. [Czyzowicz et al., Proc. ESA 2011].

KW - Algorithms

KW - Boundary patrolling

KW - Idleness

KW - Mobile robots

UR - http://www.scopus.com/inward/record.url?scp=84883511327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883511327&partnerID=8YFLogxK

U2 - 10.1145/2486159.2486176

DO - 10.1145/2486159.2486176

M3 - Conference contribution

AN - SCOPUS:84883511327

SN - 9781450315722

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 241

EP - 250

BT - SPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013

Y2 - 23 July 2013 through 25 July 2013

ER -