### 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 |
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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 | |

Publication status | Published - Jan 1 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) |
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Volume | 8986 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 25th International Workshop on Combinatorial Algorithms, IWOCA 2014 |
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Country | United States |

City | Duluth |

Period | 10/15/14 → 10/17/14 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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