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Fast and Compact Prefix Codes

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SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5901))

Abstract

It is well-known that, given a probability distribution over n characters, in the worst case it takes Θ(n logn) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for any ε with 0 < ε< 1/2 and 1 /ε = O(polylog(n)), it takes O(n loglog(1 / ε)) bits to store a prefix code with expected codeword length within an additive ε of the minimum. We then show that, for any constant c > 1, it takes O(n 1 / c logn) bits to store a prefix code with expected codeword length at most c times the minimum. In both cases, our data structures allow us to encode and decode any character in O(1) time.

Funded in part by Millennium Institute for Cell Dynamics and Biotechnology (ICDB), Grant ICM P05-001-F, Mideplan, Chile.

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Author information

Authors and Affiliations

  1. Research Group in Genome Informatics, Bielefeld University,  

    Travis Gagie

  2. Department of Computer Science, University of Chile,  

    Travis Gagie & Gonzalo Navarro

  3. Department of Computer Science, University of Bonn,  

    Yakov Nekrich

Authors
  1. Travis Gagie
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  2. Gonzalo Navarro
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  3. Yakov Nekrich
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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© 2010 Springer-Verlag Berlin Heidelberg

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Gagie, T., Navarro, G., Nekrich, Y. (2010). Fast and Compact Prefix Codes. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_35

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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