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Efficient Implementation of the WARM-UP Algorithm for the Construction of Length-Restricted Prefix Codes

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Algorithm Engineering and Experimentation (ALENEX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1619))

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Abstract

Given an alphabet ∑ = {a 1. . ., a n} with a corresponding list of positive weights {w 1, . . ., w n} and a length restriction L, the length-restricted prefix code problem is to find, a prefix code that minimizes ∑ ni=1 w i l i, where l i, the length of the codeword assigned to ai, cannot be greater than L, for i = 1, . . ., n. In this paper, we present an efficient implementation of the WARM-UP algorithm, an approximative method for this problem. The worst-case time complexity of WARM-UP is O(n log n+n logw n), where w n is the greatest weight. However, some experiments with a previous implementation of WARM-UP show that it runs in linear time for several practical cases, if the input weights are already sorted. In addition, it often produces optimal codes. The proposed implementation combines two new enhancements to reduce the space usage of WARM-UP and to improve its execution time. As a result, it is about ten times faster than the previous implementation of WARM-UP and overcomes the LRR Package Method, the faster known exact method.

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Author information

Authors and Affiliations

  1. Pontifícia Universidade Católica do Rio de Janeiro, Brazil

    Ruy Luiz Milidiú, Artur Alves Pessoa & Eduardo Sany Laber

Authors
  1. Ruy Luiz Milidiú
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  2. Artur Alves Pessoa
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  3. Eduardo Sany Laber
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Editor information

Editors and Affiliations

  1. Department of Computer Science, John Hopkins University, Baltimore, MD, 21218, USA

    Michael T. Goodrich

  2. Department of Mathematics and Computer Science, Amherst University, Amherst, MA, 01002, USA

    Catherine C. McGeoch

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© 1999 Springer-Verlag Berlin Heidelberg

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Milidiú, R.L., Pessoa, A.A., Laber, E.S. (1999). Efficient Implementation of the WARM-UP Algorithm for the Construction of Length-Restricted Prefix Codes. In: Goodrich, M.T., McGeoch, C.C. (eds) Algorithm Engineering and Experimentation. ALENEX 1999. Lecture Notes in Computer Science, vol 1619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48518-X_1

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  • DOI: https://doi.org/10.1007/3-540-48518-X_1

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  • Online ISBN: 978-3-540-48518-6

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