Approximation and hardness results for the maximum edges in transitive closure problem

ADAMASZEK, Anna, G. BLIN and Alexandru POPA. Approximation and hardness results for the maximum edges in transitive closure problem. In 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, LNCS 8986. Duluth; United States: Springer, 2015, p. 13-23. ISBN 978-3-319-19314-4. Available from: https://dx.doi.org/10.1007/978-3-319-19315-1_2.

Basic information

• Original name: Approximation and hardness results for the maximum edges in transitive closure problem
• Authors: ADAMASZEK, Anna (616 Poland), G. BLIN (250 France) and Alexandru POPA (642 Romania, belonging to the institution).
• Edition: Duluth; United States, 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, LNCS 8986, p. 13-23, 11 pp. 2015.
• Publisher: Springer

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: Switzerland
• Confidentiality degree: is not subject to a state or trade secret
• Publication form: printed version "print"
• Impact factor: Impact factor: 0.402 in 2005
• RIV identification code: RIV/00216224:14330/15:00087423
• Organization unit: Faculty of Informatics
• ISBN: 978-3-319-19314-4
• ISSN: 0302-9743
• Doi: http://dx.doi.org/10.1007/978-3-319-19315-1_2
• UT WoS: 000365044500002
• Keywords in English: Algorithms; Bioinformatics; Combinatorial mathematics; Graph theory; Hardness
• Tags: firank_B

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-eps, for any constant eps > 0. Additionally, we show that the problem is APXhard 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 [formula presented]