TY - GEN

T1 - Approximation and hardness results for the maximum edges in transitive closure problem

AU - Adamaszek, Anna

AU - Blin, Guillaume

AU - Popa, Alexandru

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=84937394799&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937394799&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-19315-1_2

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

M3 - Conference contribution

AN - SCOPUS:84937394799

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 13

EP - 23

BT - Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers

A2 - Froncek, Dalibor

A2 - Kratochvíl, Jan

A2 - Miller, Mirka

PB - Springer Verlag

T2 - 25th International Workshop on Combinatorial Algorithms, IWOCA 2014

Y2 - 15 October 2014 through 17 October 2014

ER -