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On the advice complexity of the set cover problem
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
2012 (English)In: Computer Science - Theory and Applications, Springer Berlin/Heidelberg, 2012, Vol. 7353 LNCS, 241-252 p.Conference paper, Published paper (Refereed)
Abstract [en]

Recently, a new approach to get a deeper understanding of online computation has been introduced: the study of the advice complexity of online problems. The idea is to measure the information that online algorithms need to be supplied with to compute high-quality solutions and to overcome the drawback of not knowing future input requests. In this paper, we study the advice complexity of an online version of the well-known set cover problem introduced by Alon et al.: for a ground set of size n and a set family of m subsets of the ground set, we obtain bounds in both n and m. We prove that a linear number of advice bits is both sufficient and necessary to perform optimally. Furthermore, for any constant c, we prove that n - c bits are enough to construct a c-competitive online algorithm and this bound is tight up to a constant factor (only depending on c). Moreover, we show that a linear number of advice bits is both necessary and sufficient to be optimal with respect to m, as well. We further show lower and upper bounds for achieving c-competitiveness also in m.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2012. Vol. 7353 LNCS, 241-252 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 7353
Keyword [en]
Advice complexity, Constant factors, High-quality solutions, Lower and upper bounds, On-line algorithms, Online computations, Online problems, Online versions, Set cover problem, Algorithms, Competition, Computation theory
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-103660DOI: 10.1007/978-3-642-30642-6_23Scopus ID: 2-s2.0-84865559124ISBN: 978-364230641-9 (print)OAI: oai:DiVA.org:kth-103660DiVA: diva2:561291
Conference
7th International Computer Science Symposium in Russia on Computer Science - Theory and Applications, CSR 2012; Nizhny Novgorod;3 July 2012 through 7 July 2012
Note

QC 20121018

Available from: 2012-10-18 Created: 2012-10-17 Last updated: 2012-10-18Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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