On the Cooperative Graph Searching Problem

In this paper, we introduce a new variation of graph searching problem, namely, cooperative graph searching problem. We define that a searcher is isolated if there is no other searchers on its close neighborhood. In this variant, we add an additional constrain that every searcher would not be isolated after each searching step. Therefore, we can make sure that every searcher can be cooperated by another searcher. We prove that the cooperative graph searching problem is NP-complete on general graphs and propose polynomial-time algorithms for the problem on grid graphs.