License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2012.249
URN: urn:nbn:de:0030-drops-38639
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3863/
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Kumar, Amit ; Panda, Preeti R. ; Sarangi, Smruti

Efficient on-line algorithm for maintaining k-cover of sparse bit-strings

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Abstract

We consider the on-line problem of representing a sparse bit string by a set of k intervals, where k is much smaller than the length of the string. The goal is to minimize the total length of these intervals under the condition that each 1-bit must be in one of these intervals. We give an efficient greedy algorithm which takes time O(log k) per update (an update involves converting a 0-bit to a 1-bit), which is independent of the size of the entire string.
We prove that this greedy algorithm is 2-competitive. We use
a natural linear programming relaxation for this problem, and analyze the algorithm by finding a dual feasible solution whose value matches the cost of the greedy algorithm.

BibTeX - Entry

@InProceedings{kumar_et_al:LIPIcs:2012:3863,
  author =	{Amit Kumar and Preeti R. Panda and Smruti Sarangi},
  title =	{{Efficient on-line algorithm for maintaining k-cover of sparse bit-strings}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{249--256},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2012/3863},
  URN =		{urn:nbn:de:0030-drops-38639},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.249},
  annote =	{Keywords: On-line algorithms, string algorithms}
}

Keywords: On-line algorithms, string algorithms
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 14.12.2012

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