Scanning networks with cactus topology

The family of pursuit and evasion problems is widely studied because of its numerous practical applications, ranging from communication protocols to cybernetic and physical security. Calculating the search number of a graph is one of most commonly analyzed members of this problem family. The search number is the smallest number of mobile agents required to capture an invisible and arbitrarily fast fugitive, for instance piece of malicious software, in a given graph. It is closely related to some other well known graph parameters, such as treewidth and pathwidth, and has been studied in a wide range of variants (edge, node, mixed, monotonous, connected, distributed, and others). Calculating the edge search number of a general graph is NP-hard, while it can be computed in linear time for trees. Calculating the search number of cacti, however, has not yet been widely covered. In this work we focus on this class of graphs, as it may be used to model token ring networks as well as some other network topologies when we assume that backup links are present. We address the problem of calculating the search number, as well as generating search strategy for cacti.