Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

TL;DR

This paper provides a comprehensive experimental comparison of various fixed-parameter and branching algorithms for the Feedback Vertex Set problem, highlighting the performance differences and potential of relaxation-based approaches.

Contribution

It offers the first extensive experimental evaluation of parameterized algorithms for Feedback Vertex Set, including analysis of relaxation-based methods.

Findings

Relaxation-based approaches outperform classic algorithms in some cases

Significant performance variation among different fixed-parameter algorithms

Experimental results guide future algorithm development for Feedback Vertex Set

Abstract

Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter tractability, Feedback Vertex Set is one of the landmark problems: a long line of study resulted in multiple algorithmic approaches and deep understanding of the combinatorics of the problem. Because of its central role in parameterized complexity, the first edition of the Parameterized Algorithms and Computational Experiments Challenge (PACE) in 2016 featured Feedback Vertex Set as the problem of choice in one of its tracks. The results of PACE 2016 on one hand showed large discrepancy between performance of different classic approaches to the problem, and on the other hand indicated a new approach based on half-integral relaxations of the problem as probably the most efficient approach to the problem. In this paper we provide an exhaustive experimental evaluation of fixed-parameter and branching algorithms for Feedback Vertex Set.