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DOI: 10.4230/LIPIcs.FSTTCS.2012.249

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

Authors: Amit Kumar, Preeti R. Panda, and Smruti Sarangi

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

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.

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Amit Kumar, Preeti R. Panda, and Smruti Sarangi. Efficient on-line algorithm for maintaining k-cover of sparse bit-strings. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 249-256, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{kumar_et_al:LIPIcs.FSTTCS.2012.249,
  author =	{Kumar, Amit and Panda, Preeti R. and Sarangi, Smruti},
  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 =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.249},
  URN =		{urn:nbn:de:0030-drops-38639},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.249},
  annote =	{Keywords: On-line algorithms, string algorithms}
}

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

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