Boundary patrolling by mobile agents with distinct maximal speeds

Jurek Czyzowicz, Leszek Ga̧sieniec, Adrian Kosowski, Evangelos Kranakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 Scopus citations


A set of k mobile agents are placed on the boundary of a simply connected planar object represented by a cycle of unit length. Each agent has its own predefined maximal speed, and is capable of moving around this boundary without exceeding its maximal speed. The agents are required to protect the boundary from an intruder which attempts to penetrate to the interior of the object through a point of the boundary, unknown to the agents. The intruder needs some time interval of length τ to accomplish the intrusion. Will the intruder be able to penetrate into the object, or is there an algorithm allowing the agents to move perpetually along the boundary, so that no point of the boundary remains unprotected for a time period τ? Such a problem may be solved by designing an algorithm which defines the motion of agents so as to minimize the idle time I, i.e., the longest time interval during which any fixed boundary point remains unvisited by some agent, with the obvious goal of achieving I < τ. Depending on the type of the environment, this problem is known as either boundary patrolling or fence patrolling in the robotics literature. The most common heuristics adopted in the past include the cyclic strategy, where agents move in one direction around the cycle covering the environment, and the partition strategy, in which the environment is partitioned into sections patrolled separately by individual agents. This paper is, to our knowledge, the first study of the fundamental problem of boundary patrolling by agents with distinct maximal speeds. In this scenario, we give special attention to the performance of the cyclic strategy and the partition strategy. We propose general bounds and methods for analyzing these strategies, obtaining exact results for cases with 2, 3, and 4 agents. We show that there are cases when the cyclic strategy is optimal, cases when the partition strategy is optimal and, perhaps more surprisingly, novel, alternative methods have to be used to achieve optimality.

Original languageEnglish (US)
Title of host publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Number of pages12
StatePublished - Sep 20 2011
Externally publishedYes
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: Sep 5 2011Sep 9 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th Annual European Symposium on Algorithms, ESA 2011


  • boundary patrolling
  • fence patrolling
  • idleness
  • mobile agents

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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