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Solving 3-Superstring in 3n/3 Time

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Mathematical Foundations of Computer Science 2013 (MFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8087))

Abstract

In the shortest common superstring problem (SCS) one is given a set s 1, …, s n of n strings and the goal is to find a shortest string containing each s i as a substring. While many approximation algorithms for this problem have been developed, it is still not known whether it can be solved exactly in fewer than 2n steps. In this paper we present an algorithm that solves the special case when all of the input strings have length 3 in time 3n/3 and polynomial space. The algorithm generates a combination of a de Bruijn graph and an overlap graph, such that a SCS is then a shortest directed rural postman path (DRPP) on this graph. We show that there exists at least one optimal DRPP satisfying some natural properties. The algorithm works basically by exhaustive search, but on the reduced search space of such paths of size 3n/3.

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Author information

Authors and Affiliations

  1. New York University, USA

    Alexander Golovnev

  2. St. Petersburg Department of Steklov, Institute of Mathematics, USA

    Alexander S. Kulikov

  3. Algorithmic Biology Laboratory, St. Petersburg Academic University, USA

    Alexander S. Kulikov

  4. St. Petersburg Academic University, USA

    Ivan Mihajlin

Authors
  1. Alexander Golovnev
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  2. Alexander S. Kulikov
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  3. Ivan Mihajlin
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Editor information

Editors and Affiliations

  1. Institute for Science and Technology, 3400, Klosterneuburg, Austria

    Krishnendu Chatterjee

  2. Charles University, 11800, Prague, Czech Republic

    Jirí Sgall

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Golovnev, A., Kulikov, A.S., Mihajlin, I. (2013). Solving 3-Superstring in 3n/3 Time. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_43

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  • DOI: https://doi.org/10.1007/978-3-642-40313-2_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40312-5

  • Online ISBN: 978-3-642-40313-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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