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

Anna Adamaszek, Guillaume Blin, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationCombinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers
PublisherSpringer Verlag
Pages13-23
Number of pages11
Volume8986
ISBN (Print)9783319193144
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States
Duration: Oct 15 2014Oct 17 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8986
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other25th International Workshop on Combinatorial Algorithms, IWOCA 2014
CountryUnited States
CityDuluth
Period10/15/1410/17/14

Fingerprint

Transitive Closure
Approximation algorithms
Hardness
Coloring
Approximation
Computational complexity
Approximation Algorithms
Color
Computational Biology
Graph in graph theory
Connected Components
Undirected Graph
Colouring
Complement
NP-complete problem
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Adamaszek, A., Blin, G., & Popa, A. (2015). Approximation and hardness results for the maximum edges in transitive closure problem. In Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers (Vol. 8986, 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. Vol. 8986 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 proceedingConference contribution

Adamaszek, A, Blin, G & Popa, A 2015, Approximation and hardness results for the maximum edges in transitive closure problem. in Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. vol. 8986, 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 Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers. Vol. 8986. 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. Vol. 8986 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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