Algorithmic and Hardness Results for the Colorful Components
Problems

D 2014

Algorithmic and Hardness Results for the Colorful Components Problems

ADAMASZEK, Anna and Alexandru POPA

Basic information

Original name

Algorithmic and Hardness Results for the Colorful Components Problems

Authors

ADAMASZEK, Anna (620 Portugal) and Alexandru POPA (642 Romania, guarantor, belonging to the institution)

Edition

Berlin, 11th Latin American Theoretical Informatics Symposium, LATIN 2014, p. 683-694, 12 pp. 2014

Publisher

Springer

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

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/00216224:14330/14:00080117

Organization unit

Faculty of Informatics

ISBN

978-3-642-54422-4

ISSN

DOI

http://dx.doi.org/10.1007/978-3-642-54423-1_59

UT WoS

000342804300059

Keywords in English

Algorithms; Information science; Polynomial approximation

Abstract

V originále

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 C' 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 not equal 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 vertical bar V vertical bar(1/14-epsilon) for any epsilon > 0, assuming P not equal NP (or within a factor of vertical bar V vertical bar(1/2-epsilon), assuming ZPP not equal NP).

Links

EE2.3.30.0009, research and development project

Name: Zaměstnáním čerstvých absolventů doktorského studia k vědecké excelenci

Citovat

ADAMASZEK, Anna and Alexandru POPA. Algorithmic and Hardness Results for the Colorful Components Problems. In 11th Latin American Theoretical Informatics Symposium, LATIN 2014. Berlin: Springer, 2014, p. 683-694. ISBN 978-3-642-54422-4. Available from: https://dx.doi.org/10.1007/978-3-642-54423-1_59.

@inproceedings{1298543,
   author = {Adamaszek, Anna and Popa, Alexandru},
   address = {Berlin},
   booktitle = {11th Latin American Theoretical Informatics Symposium, LATIN 2014},
   doi = {http://dx.doi.org/10.1007/978-3-642-54423-1_59},
   keywords = {Algorithms; Information science; Polynomial approximation},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Berlin},
   isbn = {978-3-642-54422-4},
   pages = {683-694},
   publisher = {Springer},
   title = {Algorithmic and Hardness Results for the Colorful Components Problems},
   year = {2014}
}

TY  - JOUR
ID  - 1298543
AU  - Adamaszek, Anna - Popa, Alexandru
PY  - 2014
TI  - Algorithmic and Hardness Results for the Colorful Components Problems
PB  - Springer
CY  - Berlin
SN  - 9783642544224
KW  - Algorithms
KW  - Information science
KW  - Polynomial approximation
N2  - 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 C' 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 not equal 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 vertical bar V vertical bar(1/14-epsilon) for any epsilon > 0, assuming P not equal NP (or within a factor of vertical bar V vertical bar(1/2-epsilon), assuming ZPP not equal NP).
ER  -

ADAMASZEK, Anna and Alexandru POPA. Algorithmic and Hardness Results for the Colorful Components Problems. In \textit{11th Latin American Theoretical Informatics Symposium, LATIN 2014}. Berlin: Springer, 2014, p.~683-694. ISBN~978-3-642-54422-4. Available from: https://dx.doi.org/10.1007/978-3-642-54423-1\_{}59.

Detailed Information on Publication Record