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

Authors Amit Kumar, Preeti R. Panda, Smruti Sarangi

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  • On-line algorithms
  • string algorithms

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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.

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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) https://doi.org/10.4230/LIPIcs.FSTTCS.2012.249

Author Details

Amit Kumar
Preeti R. Panda
Smruti Sarangi
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