Exact and heuristic algorithms for Cograph Editing

TL;DR

This paper introduces an exact dynamic programming algorithm with practical speedups and a heuristic for the Cograph Editing problem, assessing its effectiveness in recovering true graphs from noisy data.

Contribution

It provides the first exact algorithm for Cograph Editing with detailed complexity analysis, along with a heuristic and an evaluation of the cograph property in data recovery.

Findings

Exact algorithm runs in $O(3^n n)$ time and uses $O(2^n)$ space.

Heuristic produces good results on small to medium datasets.

Cograph property can effectively recover true graphs from noisy data.

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.