Fast Quasi-Threshold Editing

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with a minimum number of edge insertions and deletions. Given a graph it computes a quasi-threshold graph which is close in terms of edit count, but not necessarily closest as this edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM performs well in practice and is the first heuristic 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.