Maximum vertex occupation time and inert fugitive: recontamination does help

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.

This paper has been withdrawn by the authors [arXiv admin]. The paper has been published and the final journal version has been improved by eliminating some technical errors

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