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On Shortest Common Superstring and Swap Permutations

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String Processing and Information Retrieval (SPIRE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6393))

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Abstract

The Shortest Common Superstring (SCS) is a well studied problem, having a wide range of applications. In this paper we consider two problems closely related to it. First we define the Swapped Restricted Superstring(SRS) problem, where we are given a set S of n strings, s 1, s 2, ..., s n , and a text T = t 1 t 2 ...t m , and our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the number of strings in S that are substrings of t π(1) t π(2)...t π(m). We then show that the SRS problem is NP-Complete. Afterwards, we consider a similar variant denoted SRSR, where our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the total number of times that the strings of S appear in t π(1) t π(2)...t π(m) (we can count the same string s i as a substring of t π(1) t π(2)...t π(m) more than once). For this problem, we present a polynomial time exact algorithm.

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Author information

Authors and Affiliations

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

    Zvi Gotthilf & Moshe Lewenstein

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

    Alexandru Popa

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

Editors and Affiliations

  1. School of Physics and Mathematics, Edificio "B", Universidad Michoacana, Ciudad Universitaria, 5800, Morelia, Mich., Mexico

    Edgar Chavez

  2. Dept. of Computer Science and Enginerring, University of California, 92521, Riverside, CA, USA

    Stefano Lonardi

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Gotthilf, Z., Lewenstein, M., Popa, A. (2010). On Shortest Common Superstring and Swap Permutations. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_28

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  • DOI: https://doi.org/10.1007/978-3-642-16321-0_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16320-3

  • Online ISBN: 978-3-642-16321-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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