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

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

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

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

core_B, firank_B

---

Abstract

V originále

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]