Exact and heuristic algorithms for Cograph Editing

Abstract: We present a dynamic programming algorithm for optimally solving the Cograph Editing problem on an $n$-vertex graph that runs in $O(3^n n)$ time and uses $O(2^n)$ space. In this problem, we are given a graph $G = (V, E)$ and the task is to find a smallest possible set $F \subseteq V \times V$ of vertex pairs such that $(V, E \bigtriangleup F)$ is a cograph (or $P_4$-free graph), where $\bigtriangleup$ represents the symmetric difference operator. We also describe a technique for speeding up the performance of the algorithm in practice. Additionally, we present a heuristic for solving the Cograph Editing problem which produces good results on small to medium datasets. In application it is much more important to find the ground truth, not some optimal solution. For the first time, we evaluate whether the cograph property is strict enough to recover the true graph from data to which noise has been added.