On-line and off-line approximation algorithms for vector covering problems

Noga Alon, János Csirik, Sergey V. Sevastianov, Arjen P A Vestjens, Gerhard J. Woeginger

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

3 Citations (Scopus)

Abstract

This paper deals with vector covering problems in ddimensional space. The input to a vector covering problem consists of a set X of d-dimensional vectors in [0, 1] d. The goal is to partition X into a maximum number of parts, subject to the constraint that in every part the sum of all vectors is at least one in every coordinate. This problem is known to be NP-complete, and we are mainly interested in its on-line and off-line approximability. For the on-fine version, we construct approximation algorithms with worst case guarantee arbitrarily close to 1/(2d) in d ≥ 2 dimensions. This result contradicts a statement of Csirik and Freak (1990) in [5] where it is claimed that for d ≥ 2, no on-line algorithm can have a worst case ratio better than zero. For the off-fine version, we derive polynomial time approximation algorithms with worst case guarantee Ω (1/log d). For d = 2, we present a very fast and very simple off-line approximation algorithm that has worst case ratio 1/2. Moreover, we show that a method from the area of compact vector summation can be used to construct off-line approximation algorithms with worst case ratio 1/d for every d ≥ 2.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages406-418
Number of pages13
Volume1136
ISBN (Print)3540616802, 9783540616801
DOIs
Publication statusPublished - 1996
Event4th European Symposium on Algorithms, ESA 1996 - Barcelona, Spain
Duration: Sep 25 1996Sep 27 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1136
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th European Symposium on Algorithms, ESA 1996
CountrySpain
CityBarcelona
Period9/25/969/27/96

Fingerprint

Covering Problem
Approximation algorithms
Approximation Algorithms
Line
Approximability
Summation
Polynomial-time Algorithm
NP-complete problem
Partition
Polynomials
Zero

Keywords

  • Approximation algorithm
  • Covering problem
  • On-line algorithm
  • Packing problem
  • Worst case ratio

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alon, N., Csirik, J., Sevastianov, S. V., Vestjens, A. P. A., & Woeginger, G. J. (1996). On-line and off-line approximation algorithms for vector covering problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1136, pp. 406-418). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1136). Springer Verlag. https://doi.org/10.1007/3-540-61680-2_71

On-line and off-line approximation algorithms for vector covering problems. / Alon, Noga; Csirik, János; Sevastianov, Sergey V.; Vestjens, Arjen P A; Woeginger, Gerhard J.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1136 Springer Verlag, 1996. p. 406-418 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1136).

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

Alon, N, Csirik, J, Sevastianov, SV, Vestjens, APA & Woeginger, GJ 1996, On-line and off-line approximation algorithms for vector covering problems. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1136, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1136, Springer Verlag, pp. 406-418, 4th European Symposium on Algorithms, ESA 1996, Barcelona, Spain, 9/25/96. https://doi.org/10.1007/3-540-61680-2_71
Alon N, Csirik J, Sevastianov SV, Vestjens APA, Woeginger GJ. On-line and off-line approximation algorithms for vector covering problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1136. Springer Verlag. 1996. p. 406-418. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-61680-2_71
Alon, Noga ; Csirik, János ; Sevastianov, Sergey V. ; Vestjens, Arjen P A ; Woeginger, Gerhard J. / On-line and off-line approximation algorithms for vector covering problems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1136 Springer Verlag, 1996. pp. 406-418 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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