Fractional set cover in the streaming model

Piotr Indyk, Sepideh Mahabadi, Ronitt Rubinfeld, Jonathan Ullman, Ali Vakilian, Anak Yodpinyanee

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

15 Scopus citations

Abstract

We study the Fractional Set Cover problem in the streaming model. That is, we consider the relaxation of the set cover problem over a universe of n elements and a collection of m sets, where each set can be picked fractionally, with a value in [0, 1]. We present a randomized (1+)- approximation algorithm that makes p passes over the data, and uses eO(mnO(1/p) +n) memory space. The algorithm works in both the set arrival and the edge arrival models. To the best of our knowledge, this is the first streaming result for the fractional set cover problem. We obtain our results by employing the multiplicative weights update framework in the streaming settings.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 20th International Workshop, APPROX 2017 and 21st International Workshop, RANDOM 2017
EditorsJose D. P. Rolim, Klaus Jansen, David P. Williamson, Santosh S. Vempala
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770446
DOIs
StatePublished - 1 Aug 2017
Externally publishedYes
Event20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2017 and the 21st International Workshop on Randomization and Computation, RANDOM 2017 - Berkeley, United States
Duration: 16 Aug 201718 Aug 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume81
ISSN (Print)1868-8969

Conference

Conference20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2017 and the 21st International Workshop on Randomization and Computation, RANDOM 2017
Country/TerritoryUnited States
CityBerkeley
Period16/08/1718/08/17

Funding

FundersFunder number
Royal Thai Government
National Science Foundation
Iowa Science Foundation1536/14, CCF-1420692, CCF-1065125, CCF-1650733
Israel Science Foundation

    Keywords

    • Fractional Set Cover
    • LP relaxation
    • Multiplicative Weight Update
    • Streaming Algorithms

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