Complexity and parameterized algorithms for Cograph Editing

Authors:
Yunlong Liu;Jianxin Wang;Jiong Guo;Jianer Chen
Affiliations:
School of Mathematics and Computer Science, Hunan Normal University, Changsha 410013, PR China;School of Information Science and Engineering, Central South University, Changsha 410083, PR China;Universität des Saarlandes, Campus E 1.7, D-66123, Saarbrücken, Germany;School of Information Science and Engineering, Central South University, Changsha 410083, PR China and Department of Computer Science,Texas A&M University, College Station, TX77843-3112, USA
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

Cograph Editing is to find for a given graph G=(V,E) a set of at most k edge additions and deletions that transform G into a cograph. The computational complexity of this problem was open in the past. In this paper, we first show that this problem is NP-hard by a reduction from Exact 3-Cover. Subsequently, we present a parameterized algorithm based on a refined search tree technique with a running time of O(4.612^k+|V|^4^.^5), which improves the trivial algorithm of running time O(6^k+|V|^4^.^5).