Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

Krzysztof Kiljan, Marcin Pilipczuk, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
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
more » ... on 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. ACM Subject Classification Theory of computation → Parameterized complexity and exact algorithms, Theory of computation → Graph algorithms analysis Keywords and phrases Empirical Evaluation of Algorithms, Feedback Vertex Set Digital Object Identifier 10.4230/LIPIcs.SEA.2018.12 Funding Supported by the "Recent trends in kernelization: theory and experimental evaluation" project, carried out within the Homing programme of the Foundation for Polish Science cofinanced by the European Union under the European Regional Development Fund. Feedback Vertex Set is one of the most-studied problems from the point of view of parameterized algorithms. A long line of research [4,
doi:10.4230/lipics.sea.2018.12 dblp:conf/wea/KiljanP18 fatcat:symgz3xuzfffzphp5jkzox3qwy