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Explicit Inapproximability Bounds for the Shortest Superstring Problem

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Mathematical Foundations of Computer Science 2005 (MFCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3618))

Abstract

Given a set of strings S = {s 1,..., s n }, the Shortest Superstring problem asks for the shortest string s which contains each s i as a substring. We consider two measures of success in this problem: the length measure, which is the length of s, and the compression measure, which is the difference between the sum of lengths of the s i and the length of s. Both the length and the compression versions of the problem are known to be MAX-SNP-hard. The only explicit approximation ratio lower bounds are by Ott: 1.000057 for the length measure and 1.000089 for the compression measure. Using a natural construction we improve these lower bounds to 1.00082 for the length measure and 1.00093 for the compression measure. Our lower bounds hold even for instances in which the strings are over a binary alphabet and have equal lengths. In fact, we show a somewhat surprising result, that the Shortest Superstring problem (with respect to both measures) is as hard to approximate on instances over a binary alphabet, as it is over any alphabet.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Virginia Vassilevska

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  1. Virginia Vassilevska
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Editors and Affiliations

  1. Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80 952, Gdansk, Poland

    Joanna Jȩdrzejowicz  & Andrzej Szepietowski  & 

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Vassilevska, V. (2005). Explicit Inapproximability Bounds for the Shortest Superstring Problem. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_68

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  • DOI: https://doi.org/10.1007/11549345_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28702-5

  • Online ISBN: 978-3-540-31867-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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