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

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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)


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
  • Set Cover
  • Delay
  • Clairvoyant


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