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

Anna Adamaszek; Guillaume Blin; Alexandru Popa

doi:10.1007/978-3-319-19315-1_2

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

Anna Adamaszek, Guillaume Blin, Alexandru Popa

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

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−ε, for any constant ε > 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].

Original language	English
Title of host publication	Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers
Editors	Dalibor Froncek, Jan Kratochvíl, Mirka Miller
Publisher	Springer Verlag
Pages	13-23
Number of pages	11
ISBN (Electronic)	9783319193144
DOIs	https://doi.org/10.1007/978-3-319-19315-1_2
Publication status	Published - 2015
Event	25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States Duration: Oct 15 2014 → Oct 17 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8986
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	25th International Workshop on Combinatorial Algorithms, IWOCA 2014
Country	United States
City	Duluth
Period	10/15/14 → 10/17/14

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-319-19315-1_2

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Adamaszek, A., Blin, G., & Popa, A. (2015). Approximation and hardness results for the maximum edges in transitive closure problem. In D. Froncek, J. Kratochvíl, & M. Miller (Eds.), Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers (pp. 13-23). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986). Springer Verlag. https://doi.org/10.1007/978-3-319-19315-1_2

Approximation and hardness results for the maximum edges in transitive closure problem. / Adamaszek, Anna; Blin, Guillaume; Popa, Alexandru.

Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. ed. / Dalibor Froncek; Jan Kratochvíl; Mirka Miller. Springer Verlag, 2015. p. 13-23 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Adamaszek, A, Blin, G & Popa, A 2015, Approximation and hardness results for the maximum edges in transitive closure problem. in D Froncek, J Kratochvíl & M Miller (eds), Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8986, Springer Verlag, pp. 13-23, 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, Duluth, United States, 10/15/14. https://doi.org/10.1007/978-3-319-19315-1_2

Adamaszek A, Blin G, Popa A. Approximation and hardness results for the maximum edges in transitive closure problem. In Froncek D, Kratochvíl J, Miller M, editors, Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. Springer Verlag. 2015. p. 13-23. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-19315-1_2

Adamaszek, Anna ; Blin, Guillaume ; Popa, Alexandru. / Approximation and hardness results for the maximum edges in transitive closure problem. Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. editor / Dalibor Froncek ; Jan Kratochvíl ; Mirka Miller. Springer Verlag, 2015. pp. 13-23 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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−ε, for any constant ε > 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].",

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

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