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Restricted Common Superstring and Restricted Common Supersequence

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Combinatorial Pattern Matching (CPM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6661))

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Abstract

The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq). In the RCSstr (RCSseq) problem we are given a set S of n strings, s 1, s 2, …, s n , and a multiset t = {t 1, t 2, …, t m }, and the goal is to find a permutation π: {1, …, m} → {1, …, m} to maximize the number of strings in S that are substrings (subsequences) of π(t) = t π(1) t π(2) ⋯ t π(m) (we call this ordering of the multiset, π(t), a permutation of t). We first show that in its most general setting the RCSstr problem is NP-complete and hard to approximate within a factor of n 1 − ε, for any ε > 0, unless P = NP. Afterwards, we present two separate reductions to show that the RCSstr problem remains NP-Hard even in the case where the elements of t are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the RCSstr problem. In the second part of this paper, we turn to the RCSseq problem, where we present some hardness results, tight lower bounds and approximation algorithms.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bristol, UK

    Raphaël Clifford & Alexandru Popa

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, 52900, Israel

    Zvi Gotthilf & Moshe Lewenstein

Authors
  1. Raphaël Clifford
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  2. Zvi Gotthilf
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  3. Moshe Lewenstein
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  4. Alexandru Popa
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Università degli Studi di Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Raffaele Giancarlo

  2. Department of Computer Science, University of ’Piemonte Orientale’, Viale T. Michel 11, 15121, Alessandria, Italy

    Giovanni Manzini

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© 2011 Springer-Verlag Berlin Heidelberg

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Clifford, R., Gotthilf, Z., Lewenstein, M., Popa, A. (2011). Restricted Common Superstring and Restricted Common Supersequence. In: Giancarlo, R., Manzini, G. (eds) Combinatorial Pattern Matching. CPM 2011. Lecture Notes in Computer Science, vol 6661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21458-5_39

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  • DOI: https://doi.org/10.1007/978-3-642-21458-5_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21457-8

  • Online ISBN: 978-3-642-21458-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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