Set cover with delay – Clairvoyance is not required

Yossi Azar, Ashish Chiplunkar, Shay Kutten, Noam Touitou

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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).

Original languageEnglish
Title of host publication28th Annual European Symposium on Algorithms, ESA 2020
EditorsFabrizio Grandoni, Grzegorz Herman, Peter Sanders
ISBN (Electronic)9783959771627
DOIs
StatePublished - 1 Aug 2020
Event28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, Italy
Duration: 7 Sep 20209 Sep 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume173

Conference

Conference28th Annual European Symposium on Algorithms, ESA 2020
Country/TerritoryItaly
CityVirtual, Pisa
Period7/09/209/09/20

Keywords

  • Clairvoyant
  • Delay
  • Set Cover

All Science Journal Classification (ASJC) codes

  • Software

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