A fast and space-economical algorithm for length-limited coding

  • Jyrki Katajainen
  • Alistair Moffat
  • Andrew Turpin
Session 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1004)

Abstract

The minimum-redundancy prefix code problem is to determine a list of integer codeword lengths l=[li¦{1... n}], given a list of n symbol weights p=[pi¦{1...n}], such that \(\sum\nolimits_{i = 1}^n {2^{ - l_i } } \leqslant 1\), and \(\sum\nolimits_{i = 1}^n {l_i p_i }\)lipi is minimised. An extension is the minimum-redundancy length-limited prefix code problem, in which the further constraint li≤L is imposed, for all i ε {1... n} and some integer L≥[log2n]. The package-merge algorithm of Larmore and Hirschberg generates length-limited codes in O(nL) time using O(n) words of auxiliary space. Here we show how the size of the work space can be reduced to O(L2). This represents a useful improvement, since for practical purposes L is Θ(log n).

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jyrki Katajainen
    • 1
  • Alistair Moffat
    • 2
  • Andrew Turpin
    • 2
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagen EastDenmark
  2. 2.Department of Computer ScienceThe University of MelbourneParkvilleAustralia

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