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On the Approximation Ratio of the Group-Merge Algorithm for the Shortest Common Superstring Problem

  • Dirk Bongartz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1963)

Abstract

The shortest common superstring problem (SCS) is one of the fundamental optimization problems in the area of data compression and DNA sequencing. The SCS is known to be APX-hard [1]. This paper focuses on the analysis of the approximation ratio of two greedy-based approximation algorithms for it, namely the naive Greedy algorithm and the Group-Merge algorithm. The main results of this paper are: (i) We disprove the claim that the input instances of Jiang and Li [4] prove that the Group-Merge algorithm does not provide any constant approximation for the SCS. We even prove that the Group-Merge algorithm always finds optimal solutions for these instances. (ii) We show that the Greedy algorithm and the Group-Merge algorithm are incomparable according to the approximation ratio. (iii) We attack the main problem whether the Group-Merge algorithm has a constant approximation ratio by showing that this is the case for a slightly modified algorithm denoted as Group-Merge-1 if all strings have approximately the same length and the compression is limited by a constant fraction of the trivial solution.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Dirk Bongartz
    • 1
  1. 1.Lehrstuhl für Informatik IRWTH AachenAachenGermany

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