Patrolling on Dynamic Ring Networks

TL;DR

This paper introduces algorithms for collaborative patrolling of dynamic ring networks, achieving near-optimal coverage times and highlighting the impact of prior knowledge on patrol efficiency.

Contribution

It presents the first algorithms for multi-agent patrolling on dynamic graphs, with bounds close to optimal and a comparison of knowledge assumptions.

Findings

Algorithms achieve near-optimal idle time.

Prior knowledge significantly improves patrol efficiency.

First known results for patrolling on dynamic graphs.

Abstract

We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every $I(n)$ time units, with the objective of minimizing the idle time $I(n)$. While patrolling has been studied previously for static networks, we investigate the problem on dynamic networks with a fixed set of nodes, but dynamic edges. In particular, we consider 1-interval-connected ring networks and provide various patrolling algorithms for such networks, for $k=2$ or $k>2$ agents. We also show almost matching lower bounds that hold even for the best starting configurations. Thus, our algorithms achieve close to optimal idle time. Further, we show a clear separation in terms of idle time, for agents that have prior knowledge of the dynamic networks compared to agents that do not have such knowledge. This paper provides the first known results for collaborative patrolling on dynamic graphs.