A Faster Parameterized Algorithm for Group Feedback Edge Set

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9941)

Abstract

In the Group Feedback Edge Set (\(\ell \)) (Group FES(\(\ell \))) problem, the input is a group-labeled graph G over a group \(\varGamma \) of order \(\ell \) and an integer k and the objective is to test whether there exists a set of at most k edges intersecting every non-null cycle in G. The study of the parameterized complexity of Group FES(\(\ell \)) was motivated by the fact that it generalizes the classical Edge Bipartization problem when \(\ell =2\). Guillemot [IWPEC 2008, Discrete Optimization 2011] initiated the study of the parameterized complexity of this problem and proved that it is fixed-parameter tractable (FPT) parameterized by k. Subsequently, Wahlström [SODA 2014] and Iwata et al. [2014] presented algorithms running in time \({\mathcal {O}}(4^kn^{{\mathcal {O}}(1)})\) (even in the oracle access model) and \({\mathcal {O}}(\ell ^{2k}m)\) respectively. In this paper, we give an algorithm for Group FES(\(\ell \)) running in time \({\mathcal {O}}(4^kk^{3}\ell (m+n))\). Our algorithm matches that of Iwata et al. when \(\ell =2\) (upto a multiplicative factor of \(k^3\)) and gives an improvement for \(\ell >2\).

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Copyright information

© Springer-Verlag GmbH Germany 2016

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria

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