Computing a Feedback Arc Set Using PageRank

TL;DR

This paper introduces a heuristic algorithm for finding minimum Feedback Arc Sets in directed graphs, leveraging PageRank scores on the line graph to produce significantly better solutions efficiently.

Contribution

The paper presents a novel heuristic that uses PageRank on the line graph to improve Feedback Arc Set solutions over previous methods.

Findings

Reduces FAS size by over 50% compared to previous heuristics

Runs efficiently on large graphs used in graph drawing

Produces better solutions than existing heuristics

Abstract

We present a new heuristic algorithm for computing a minimum Feedback Arc Set in directed graphs. The new technique produces solutions that are better than the ones produced by the best previously known heuristics, often reducing the FAS size by more than 50%. It is based on computing the PageRank score of the nodes of the directed line graph of the input directed graph. Although the time required by our heuristic is heavily influenced by the size of the produced line graph, our experimental results show that it runs very fast even for very large graphs used in graph drawing.