Effective Computation of a Feedback Arc Set Using PageRank

Abstract

Computing a minimum Feedback Arc Set (FAS) is important for visualizing directed graphs in hierarchical style. It is the first step of both known frameworks for hierarchical graph drawing of directed graphs and it is NP-hard. We present a new heuristic algorithm for computing a minimum FAS in directed graphs. The new technique produces solutions that, for graph drawing datasets, are better than the ones produced by the best previously known heuristics, often reducing the FAS size by more than 50%. The heuristic 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. We compare results produced by our heuristic to known exact results for specific graphs used in a previous study and discuss the interesting trade-off. Finally, our experimental results on large web-graphs show that our technique found smaller FAS than it was known before for some web-graphs from a data set used in a recent study.