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Parallel and sequential approximation of shortest superstrings

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Algorithm Theory — SWAT '94 (SWAT 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 824))

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Abstract

Superstrings have many applications in data compression and genetics. However the decision version of the shortest superstring problem is N P-complete. In this paper we examine the complexity of approximating a shortest superstring. There are two basic measures of the approximations: the compression ratio and the approximation ratio. The well known and practical approximation algorithm is the sequential algorithm GREEDY. It approximates the shortest superstring with the compression ratio of 1/2 and with the approximation ratio of 4. Our main results are:

  1. (1)

    An NC algorithm which achieves the compression ratio of 1/4+ε.

  2. (2)

    The proof that the algorithm GREEDY is not parallelizable, the computation of its output is P-complete.

  3. (3)

    An improved sequential algorithm: the approximation ratio is reduced to 2.83. Previously it was reduced by Teng and Yao from 3 to 2.89.

  4. (4)

    The design of an RNC algorithm with constant approximation ratio and an NC algorithm with logarithmic approximation ratio.

Supported by DFG-Graduiertenkolleg “Parallele Rechnernetzwerke in der Produktionstechnik”, ME 872/4-1.

Supported in part by the EC Cooperative Action IC 1000 Algorithms for Future Technologies “ALTEC”.

Supported in part by Alexander von Humboldt-Stiftung and Volkswagen Stiftung.

Supported in part by the ESPRIT Basic Research Action No. 7141 (ALCOM II)

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Author information

Author notes

  1. Marek Piotrów

    Present address: Instytut Informatyki, Uniwersytet Wroclawski, Przesmyckiego 20, 51-151, Wroclaw, Poland

Authors and Affiliations

  1. Heinz Nixdorf Institut, Universität-GH-Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Artur Czumaj & Marek Piotrów

  2. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02-097, Warszawa, Poland

    Leszek Gasieniec & Wojciech Rytter

Authors
  1. Artur Czumaj
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  2. Leszek Gasieniec
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  3. Marek Piotrów
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  4. Wojciech Rytter
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Editor information

Erik M. Schmidt Sven Skyum

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© 1994 Springer-Verlag Berlin Heidelberg

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Czumaj, A., Gasieniec, L., Piotrów, M., Rytter, W. (1994). Parallel and sequential approximation of shortest superstrings. In: Schmidt, E.M., Skyum, S. (eds) Algorithm Theory — SWAT '94. SWAT 1994. Lecture Notes in Computer Science, vol 824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58218-5_9

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  • DOI: https://doi.org/10.1007/3-540-58218-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58218-2

  • Online ISBN: 978-3-540-48577-3

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