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 Scopus citations

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 (US)
Title of host publicationAlgorithms - ESA 1996 - 4th Annual European Symposium, Proceedings
EditorsJosep Diaz, Maria Serna
PublisherSpringer Verlag
Pages406-418
Number of pages13
ISBN (Print)3540616802, 9783540616801
DOIs
StatePublished - Jan 1 1996
Externally publishedYes
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)0302-9743
ISSN (Electronic)1611-3349

Other

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

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

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  • 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 J. Diaz, & M. Serna (Eds.), Algorithms - ESA 1996 - 4th Annual European Symposium, Proceedings (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