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On the Advice Complexity of the Set Cover Problem

  • Dennis Komm
  • Richard Královič
  • Tobias Mömke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)

Abstract

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.

Keywords

Competitive Ratio Online Algorithm Online Computation Linear Number Online Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dennis Komm
    • 1
  • Richard Královič
    • 1
  • Tobias Mömke
    • 2
  1. 1.Department of Computer ScienceETH ZurichSwitzerland
  2. 2.School of Computer Science and CommunicationKTH Royal Institute of TechnologySweden

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