When Patrolmen Become Corrupted: Monitoring a Graph Using Faulty Mobile Robots

Czyzowicz, J, Gasieniec, L ORCID: 0000-0003-1809-9814, Kosowski, A, Kranakis, E, Krizanc, D and Taleb, N (2017) When Patrolmen Become Corrupted: Monitoring a Graph Using Faulty Mobile Robots. Algorithmica, 79 (3). pp. 925-940.

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Abstract

A team of k mobile robots is deployed on a weighted graph whose edge weights represent distances. The robots move perpetually along the domain, represented by all points belonging to the graph edges, without exceeding their maximum speed. The robots need to patrol the graph by regularly visiting all points of the domain. In this paper, we consider a team of robots (patrolmen), at most f of which may be unreliable, i.e., they fail to comply with their patrolling duties. What algorithm should be followed so as to minimize the maximum time between successive visits of every edge point by a reliable patrolman? The corresponding measure of efficiency of patrolling called idleness has been widely accepted in the robotics literature. We extend it to the case of untrusted patrolmen; we denote by Ifk(G) the maximum time that a point of the domain may remain unvisited by reliable patrolmen. The objective is to find patrolling strategies minimizing Ifk(G). We investigate this problem for various classes of graphs. We design optimal algorithms for line segments, which turn out to be surprisingly different from strategies for related patrolling problems proposed in the literature. We then use these results to study general graphs. For Eulerian graphs G, we give an optimal patrolling strategy with idleness Ifk(G)=(f+1)|E|/k, where |E| is the sum of the lengths of the edges of G. Further, we show the hardness of the problem of computing the idle time for three robots, at most one of which is faulty, by reduction from 3-edge-coloring of cubic graphs—a known NP-hard problem. A byproduct of our proof is the investigation of classes of graphs minimizing idle time (with respect to the total length of edges); an example of such a class is known in the literature under the name of Kotzig graphs.

Item Type:	Article
Uncontrolled Keywords:	Mobile robot, Fault tolerant, Patrolling, Idleness, Kotzig graphs
Depositing User:	Symplectic Admin
Date Deposited:	14 Feb 2017 13:00
Last Modified:	19 Jan 2023 07:26
DOI:	10.1007/s00453-016-0233-9
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3004376