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Algorithms for Three Versions of the Shortest Common Superstring Problem

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Combinatorial Pattern Matching (CPM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6129))

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Abstract

The input to the Shortest Common Superstring (SCS) problem is a set S of k words of total length n. In the classical version the output is an explicit word SCS(S) in which each s ∈ S occurs at least once. In our paper we consider two versions with multiple occurrences, in which the input includes additional numbers (multiplicities), given in binary. Our output is the word SCS(S) given implicitly in a compact form, since its real size could be exponential. We also consider a case when all input words are of length two, where our main algorithmic tool is a compact representation of Eulerian cycles in multigraphs. Due to exponential multiplicities of edges such cycles can be exponential and the compact representation is needed. Other tools used in our paper are a polynomial case of integer linear programming and a min-plus product of matrices.

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Author information

Authors and Affiliations

  1. King’s College London, London, WC2R 2LS, UK

    Maxime Crochemore & Costas Iliopoulos

  2. Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan, Marcin Kubica, Jakub Radoszewski, Wojciech Rytter & Tomasz Waleń

  3. Université Paris-Est, France

    Maxime Crochemore

  4. Digital Ecosystems & Business Intelligence Institute, Curtin University of Technology, Perth, WA, 6845, Australia

    Costas Iliopoulos

  5. Dept. of Math. and Informatics, Copernicus University, Toruń, Poland

    Wojciech Rytter

Authors
  1. Maxime Crochemore
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  2. Marek Cygan
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  3. Costas Iliopoulos
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  4. Marcin Kubica
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  5. Jakub Radoszewski
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  6. Wojciech Rytter
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  7. Tomasz Waleń
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA, and Bar-Ilan University, 52900, Ramat-Gan, Israel

    Amihood Amir

  2. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA

    Laxmi Parida

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© 2010 Springer-Verlag Berlin Heidelberg

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Crochemore, M. et al. (2010). Algorithms for Three Versions of the Shortest Common Superstring Problem . In: Amir, A., Parida, L. (eds) Combinatorial Pattern Matching. CPM 2010. Lecture Notes in Computer Science, vol 6129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13509-5_27

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  • DOI: https://doi.org/10.1007/978-3-642-13509-5_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13508-8

  • Online ISBN: 978-3-642-13509-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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