Minimal and stable feedback arc sets and graph centrality measures

Abstract

In this paper we tackle one of the most famous problems in graph theory and, in general, in the area of discrete optimization, namely the Minimum Feedback Arc Set Problem for a directed graph. In particular, we study the problem using the methodology of the linear arrangements of the vertices to find feedback arc sets, and an optimization heuristic to reduce their size. We test the efficacy of the heuristic against several linear arrangements of the vertices obtained by using some well known centrality metrics. We experimentally show that, independently from the linear arrangement used, our heuristic methodology obtains feedback arc sets with an average approximation ratio not greater than $\frac{1}{4}.$