Enumerating minimal subset feedback vertex sets

Authors:
Fedor V. Fomin;Pinar Heggernes;Dieter Kratsch;Charis Papadopoulos;Yngve Villanger
Affiliations:
Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway;LITA, Université Paul Verlaine, Metz, France;Department of Mathematics, University of Ioannina, Greece;Department of Informatics, University of Bergen, Norway
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

Citing 9
Cited 2

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On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

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Improved algorithms for feedback vertex set problems

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A 4k2 kernel for feedback vertex set

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Abstract

The SUBSET FEEDBACK VERTEX SET problem takes as input a weighted graph G and a vertex subset S of G, and the task is to find a set of vertices of total minimum weight to be removed from G such that in the remaining graph no cycle contains a vertex of S. This problem is a generalization of two classical NP-complete problems: FEEDBACK VERTEX SET and MULTIWAY CUT. We show that it can be solved in time O(1.8638n) for input graphs on n vertices. To the best of our knowledge, no exact algorithm breaking the trivial 2nnO(1)-time barrier has been known for SUBSET FEEDBACK VERTEX SET, even in the case of unweighted graphs. The mentioned running time is a consequence of the more general main result of this paper: we show that all minimal subset feedback vertex sets of a graph can be enumerated in O(1.8638n) time.