On Phalanx Graph Search Number

Abstract

We introduce an extension of the Connected Graph Search, called Phalanx Graph Search, which inherently emerges from the nature of certain applications. We discuss its key properties, prove NP-hardness of the problem on general graphs and introduce a linear-time algorithm for the class of trees. We exploit our analysis to examine the Minimum Phalanx Graph Search Spanning Tree Problem, again showing its hardness and investigating efficiency of certain approximations. We discuss some of our findings in relation to other search variants.