Algorithmic and hardness results for the colorful components problems

Anna Adamaszek, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph G such that in the resulting graph G' all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want G' to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial-time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is NP-hard (assuming P ≠ NP). Then, we show that the second problem is APX-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is NP-hard. Finally, we show that the third problem does not admit polynomial-time approximation within a factor of |V |1/14?∈ for any ∈ > 0, assuming P ≠ NP (or within a factor of |V

Original languageEnglish
Title of host publicationLATIN 2014
Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
PublisherSpringer Verlag
Pages683-694
Number of pages12
ISBN (Print)9783642544224
DOIs
Publication statusPublished - Jan 1 2014
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: Mar 31 2014Apr 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period3/31/144/4/14

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Adamaszek, A., & Popa, A. (2014). Algorithmic and hardness results for the colorful components problems. In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings (pp. 683-694). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_59