Maximum vertex occupation time and inert fugitive: recontamination does help

TL;DR

This paper investigates the node search problem with inert fugitive on graphs, revealing that allowing recontamination can significantly improve search efficiency by reducing maximum vertex occupation time.

Contribution

It demonstrates that non-recontamination search strategies may be suboptimal and that recontamination can arbitrarily decrease maximum vertex occupation time.

Findings

Recontamination can greatly reduce maximum vertex occupation time.

Monotone search strategies may be far from optimal.

Allowing recontamination improves search efficiency.

Abstract

Given a simple graph $G$, we consider the node search problem with inert fugitive. We are interested in minimizing the maximum vertex occupation time, i.e. the maximum number of steps in which a vertex is occupied by a searcher during a search of $G$. We prove that a search program which does not allow a recontamination may not find an optimal solution to this problem, and the difference between the maximum vertex occupation time computed by a monotone search program and a program without such restriction may be arbitrarily large.