Nearly-Tight Lower Bounds for Set Cover and Network Design with Deadlines/Delay

Noam Touitou

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

    Abstract

    In network design problems with deadlines/delay, an algorithm must make transmissions over time to satisfy connectivity requests on a graph. To satisfy a request, a transmission must be made that provides the desired connectivity. In the deadline case, this transmission must occur inside a time window associated with the request. In the delay case, the transmission should be as soon as possible after the request’s release, to avoid delay cost. In FOCS 2020, frameworks were given which reduce a network design problem with deadlines/delay to its classic, offline variant, while incurring an additional competitiveness loss factor of O(log n), where n is the number of vertices in the graph. Trying to improve upon this loss factor is thus a natural research direction. The frameworks of FOCS 2020 also apply to set cover with deadlines/delay, in which requests arrive on the elements of a universe over time, and the algorithm must transmit sets to serve them. In this problem, a universe of sets and elements is given, requests arrive on elements over time, and the algorithm must transmit sets to serve them. In this paper, we give nearly tight lower bounds for set cover with deadlines/delay. These lower bounds imply nearly-tight lower bounds of Ω(log n/log log n) for a few network design problems, such as node-weighted Steiner forest and directed Steiner tree. Our results imply that the frameworks in FOCS 2020 are essentially optimal, and improve quadratically over the best previously-known lower bounds.

    Original languageEnglish
    Title of host publication32nd International Symposium on Algorithms and Computation, ISAAC 2021
    EditorsHee-Kap Ahn, Kunihiko Sadakane
    PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
    ISBN (Electronic)9783959772143
    DOIs
    StatePublished - 1 Dec 2021
    Event32nd International Symposium on Algorithms and Computation, ISAAC 2021 - Fukuoka, Japan
    Duration: 6 Dec 20218 Dec 2021

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    Volume212
    ISSN (Print)1868-8969

    Conference

    Conference32nd International Symposium on Algorithms and Computation, ISAAC 2021
    Country/TerritoryJapan
    CityFukuoka
    Period6/12/218/12/21

    Keywords

    • Deadlines
    • Delay
    • Network design
    • Online
    • Set cover

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