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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.12
URN: urn:nbn:de:0030-drops-75613
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7561/
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Indyk, Piotr ; Mahabadi, Sepideh ; Rubinfeld, Ronitt ; Ullman, Jonathan ; Vakilian, Ali ; Yodpinyanee, Anak

Fractional Set Cover in the Streaming Model

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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+a)-approximation algorithm that makes p passes over the data, and uses O(polylog(m,n,1/a) (mn^(O(1/(pa)))+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.

BibTeX - Entry

@InProceedings{indyk_et_al:LIPIcs:2017:7561,
  author =	{Piotr Indyk and Sepideh Mahabadi and Ronitt Rubinfeld and Jonathan Ullman and Ali Vakilian and Anak Yodpinyanee},
  title =	{{Fractional Set Cover in the Streaming Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7561},
  URN =		{urn:nbn:de:0030-drops-75613},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.12},
  annote =	{Keywords: Streaming Algorithms, Fractional Set Cover, LP relaxation, Multiplicative Weight Update}
}

Keywords: Streaming Algorithms, Fractional Set Cover, LP relaxation, Multiplicative Weight Update
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 31.07.2017


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