Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find subset of at most k edges remove from so that size maximum clique, in interdicted graph, is minimized. The EICP belongs family problems with aim reducing clique number graph. optimal solutions, called policies, determine vital which are crucial for preserving its number. We propose new set-c...

Recently, new techniques have been introduced to speed up dynamic programming algorithms on tree decompositions for connectivity problems: the ‘Cut and Count’ method and a method called the rank-based approach, based on representative sets and Gaussian elimination. These methods respectively give randomised and deterministic algorithms that are single exponential in the treewidth, and polynomia...