Algorithms for testing security in graphs

Abstract

In this paper we propose new algorithmic methods giving with a high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] S| |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based on the heuristic using simulated annealing and tested it on graphs with in duced small subgraphs G[S] being trees or graphs with a bounded degree (by 3 or 4). Our approach is a generalization of the concept ofproperty testers known from the subject literature, but we applied our concepts to the coNP-complete problem.