Complexity and approximation of the connected set-cover problem

Wei Zhang, Weili Wu, Wonjun Lee, Ding Zhu Du

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we study the computational complexity and approximation complexity of the connected set-cover problem. We derive necessary and sufficient conditions for the connected set-cover problem to have a polynomial-time algorithm. We also present a sufficient condition for the existence of a (1 + ln δ)-approximation. In addition, one such (1 + ln δ)-approximation algorithm for this problem is proposed. Furthermore, it is proved that there is no polynomial-time O(log 2-ε n)-approximation for any ε > 0 for the connected set-cover problem on general graphs, unless NP has an quasi-polynomial Las-Vegas algorithm.

Original languageEnglish
Pages (from-to)563-572
Number of pages10
JournalJournal of Global Optimization
Volume53
Issue number3
DOIs
Publication statusPublished - 2012 Jul 1

Fingerprint

Set Cover
Connected Set
Polynomials
Approximation
Approximation algorithms
Sufficient Conditions
Computational complexity
Polynomial-time Algorithm
Approximation Algorithms
Polynomial time
Computational Complexity
Necessary Conditions
Polynomial
Graph in graph theory

Keywords

  • Approximation algorithms
  • Computational complexity
  • Connected set-cover

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research

Cite this

Complexity and approximation of the connected set-cover problem. / Zhang, Wei; Wu, Weili; Lee, Wonjun; Du, Ding Zhu.

In: Journal of Global Optimization, Vol. 53, No. 3, 01.07.2012, p. 563-572.

Research output: Contribution to journalArticle

Zhang, Wei ; Wu, Weili ; Lee, Wonjun ; Du, Ding Zhu. / Complexity and approximation of the connected set-cover problem. In: Journal of Global Optimization. 2012 ; Vol. 53, No. 3. pp. 563-572.
@article{2e1733ceecab4fe5b11172dfdd608cd4,
title = "Complexity and approximation of the connected set-cover problem",
abstract = "In this paper, we study the computational complexity and approximation complexity of the connected set-cover problem. We derive necessary and sufficient conditions for the connected set-cover problem to have a polynomial-time algorithm. We also present a sufficient condition for the existence of a (1 + ln δ)-approximation. In addition, one such (1 + ln δ)-approximation algorithm for this problem is proposed. Furthermore, it is proved that there is no polynomial-time O(log 2-ε n)-approximation for any ε > 0 for the connected set-cover problem on general graphs, unless NP has an quasi-polynomial Las-Vegas algorithm.",
keywords = "Approximation algorithms, Computational complexity, Connected set-cover",
author = "Wei Zhang and Weili Wu and Wonjun Lee and Du, {Ding Zhu}",
year = "2012",
month = "7",
day = "1",
doi = "10.1007/s10898-011-9726-x",
language = "English",
volume = "53",
pages = "563--572",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Complexity and approximation of the connected set-cover problem

AU - Zhang, Wei

AU - Wu, Weili

AU - Lee, Wonjun

AU - Du, Ding Zhu

PY - 2012/7/1

Y1 - 2012/7/1

N2 - In this paper, we study the computational complexity and approximation complexity of the connected set-cover problem. We derive necessary and sufficient conditions for the connected set-cover problem to have a polynomial-time algorithm. We also present a sufficient condition for the existence of a (1 + ln δ)-approximation. In addition, one such (1 + ln δ)-approximation algorithm for this problem is proposed. Furthermore, it is proved that there is no polynomial-time O(log 2-ε n)-approximation for any ε > 0 for the connected set-cover problem on general graphs, unless NP has an quasi-polynomial Las-Vegas algorithm.

AB - In this paper, we study the computational complexity and approximation complexity of the connected set-cover problem. We derive necessary and sufficient conditions for the connected set-cover problem to have a polynomial-time algorithm. We also present a sufficient condition for the existence of a (1 + ln δ)-approximation. In addition, one such (1 + ln δ)-approximation algorithm for this problem is proposed. Furthermore, it is proved that there is no polynomial-time O(log 2-ε n)-approximation for any ε > 0 for the connected set-cover problem on general graphs, unless NP has an quasi-polynomial Las-Vegas algorithm.

KW - Approximation algorithms

KW - Computational complexity

KW - Connected set-cover

UR - http://www.scopus.com/inward/record.url?scp=84863723977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863723977&partnerID=8YFLogxK

U2 - 10.1007/s10898-011-9726-x

DO - 10.1007/s10898-011-9726-x

M3 - Article

AN - SCOPUS:84863723977

VL - 53

SP - 563

EP - 572

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 3

ER -