Fast Quasi-Threshold Editing

TL;DR

This paper presents QTM, an efficient algorithm for editing large graphs into quasi-threshold graphs, demonstrating scalability and introducing a linear-time recognition method for such graphs.

Contribution

The paper introduces QTM, the first scalable algorithm for quasi-threshold graph editing on large real-world graphs, and a simple linear-time recognition algorithm.

Findings

QTM scales to large real-world graphs

QTM effectively minimizes edit distance

A linear-time recognition algorithm is proposed

Abstract

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with edge insertion and deletion. Given a graph it computes a quasi-threshold graph which is close in terms of edit count. This edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM is the first algorithm that is able to scale to large real-world graphs in practice. As a side result we further present a simple linear-time algorithm for the quasi-threshold recognition problem.