International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 13-23 | Cite as

Approximation and Hardness Results for the Maximum Edges in Transitive Closure Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

In this paper we study the following problem, named Maximum Edges in Transitive Closure, which has applications in computational biology. Given a simple, undirected graph \(G = (V,E)\) and a coloring of the vertices, remove a collection of edges from the graph such that each connected component is colorful (i.e., it does not contain two identically colored vertices) and the number of edges in the transitive closure of the graph is maximized.

The problem is known to be APX-hard, and no approximation algorithms are known for it. We improve the hardness result by showing that the problem is NP-hard to approximate within a factor of \(|V|^{1/3 - \varepsilon }\), for any constant \(\varepsilon > 0\). Additionally, we show that the problem is APX-hard already for the case when the number of vertex colors equals 3. We complement these results by showing the first approximation algorithm for the problem, with approximation factor \(\sqrt{2 \cdot \text {OPT}}\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Anna Adamaszek
    • 1
  • Guillaume Blin
    • 2
    • 3
  • Alexandru Popa
    • 4
  1. 1.Max-Planck-Institut Für InformatikSaarbrückenGermany
  2. 2.LaBRI, UMR 5800University of BordeauxTalenceFrance
  3. 3.CNRS, LaBRI, UMR 5800TalenceFrance
  4. 4.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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