Exact Computation of Minimum Feedback Vertex Sets with Relational Algebra

Authors:
Rudolf Berghammer;Alexander Fronk
Affiliations:
Institute of Computer Science and Applied Mathematics University of Kiel, D-24098 Kiel, Germany. E-mail: rub@informatik.uni-kiel.de;Software Technology University of Dortmund, D-44221 Dortmund, Germany. E-mail: alexander.fronk@uni-dortmund.de
Venue:
Fundamenta Informaticae
Year:
2006

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Abstract

A feedback vertex set of a graph is a subset of vertices containing at least one vertex from every cycle of the graph. Given a directed graph by its adjacency relation, we develop a relational algorithm for computing a feedback vertex set of minimum size. In combination with a BDD-implementation of relations, it allows to exactly solve this NP-hard problem for medium-sized graphs.