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Set Cover with Delay - Clairvoyance Is Not Required

Authors Yossi Azar, Ashish Chiplunkar, Shay Kutten, Noam Touitou

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Author Details

Yossi Azar
  • Tel Aviv University, Israel
Ashish Chiplunkar
  • Indian Institute of Technology Delhi, India
Shay Kutten
  • Technion - Israel Institute of Technology, Haifa, Israel
Noam Touitou
  • Tel Aviv University

Funding

  • Azar, Yossi: Supported in part by the Israel Science Foundation (grant No. 1506/16).
  • Chiplunkar, Ashish: Supported by Pankaj Gupta Young Faculty fellowship.
  • Kutten, Shay: Supported by the Ministry of Science and Technology together with the JSPS, as well as the BSF.

Cite AsGet BibTex

Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou. Set Cover with Delay - Clairvoyance Is Not Required. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ESA.2020.8

Abstract

In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) - specifically, we present the first non-clairvoyant algorithm, which is O(log n log m)-competitive, where n is the number of elements and m is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present lower bounds of Ω(√{log n}) and Ω(√{log m}) for SCD which apply for the clairvoyant case. In addition, the competitiveness of our algorithm does not depend on the number of requests. Such a guarantee on the size of the universe alone was not previously known even for the clairvoyant case - the only previously-known algorithm (due to Carrasco et al.) is clairvoyant, with competitiveness that grows with the number of requests. For the special case of vertex cover with delay, we show a simpler, deterministic algorithm which is 3-competitive (and also non-clairvoyant).

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Online algorithms
Keywords
  • Set Cover
  • Delay
  • Clairvoyant

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