Patrolling a Path Connecting a Set of Points with Unbalanced Frequencies of Visits

TL;DR

This paper develops approximation algorithms for two-robot patrolling on a line with divergent visit frequency constraints, improving the known approximation ratio to .

Contribution

It introduces efficient protocols for two-robot patrolling with varying frequency constraints on a line, achieving the best known approximation ratio.

Findings

Achieved a -approximation algorithm for the problem.

Extended previous models to handle divergent visit frequencies.

Provided theoretical bounds and analysis for the algorithms.

Abstract

Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the environment needed to be revisited with the same minimal frequency. In this paper we study efficient patrolling protocols for points located on a path, where each point may have a different constraint on frequency of visits. The problem of visiting such divergent points was recently posed by Gasieniec et al. in [13], where the authors study protocols using a single robot patrolling a set of $n$ points located in nodes of a complete graph and in Euclidean spaces. The focus in this paper is on patrolling with two robots. We adopt a scenario in which all points to be patrolled are located on a line. We provide several approximation algorithms concluding with the best currently known $\sqrt 3$-approximation.