Parameterized algorithms for Module Map problems

Abstract

Motivated by applications in the analysis of genetic networks, we introduce and study the NP-hard Module Map problem which has as input a graph G=(V,E) with red and blue edges and an integer k and asks to transform G by at most k edge modifications into a graph G′ which has the following properties: the vertex set of G′ can be partitioned into so-called clusters such that inside a cluster every pair of vertices is connected by a blue edge and for two distinct clusters A and B either all vertices u∈A and v∈B are connected by a red edge or there is no edge between A and B. We show that Module Map can be solved in O(3k⋅(|V|+|E|)) time and O(2k⋅|V|3) time, respectively. Furthermore, we show that Module Map admits a kernel with O(k2) vertices.