Faster Algorithm for Designing Optimal Prefix-Free Codes with Unequal Letter Costs

  • Authors:

  • Sorina Dumitrescu

  • Affiliations:

  • Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1. E-mail: sorina@mail.ece.mcmaster.ca

  • Venue:
  • Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
  • Year:
  • 2006

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Abstract

We address the problem of designing optimal prefix-free codes over an encoding alphabet with unequal integer letter costs. The most efficient algorithm proposed so far has O(n$^{C+2}$) time complexity, where n is the number of codewords and C is the maximum letter cost. For the special case when the encoding alphabet is binary, a faster solution was proposed, namely of O(n$^C$) time complexity, based on a more sophisticated modeling of the problem, and on exploiting the Monge property of the cost function. However, those techniques seemed not to extend to the r-letter alphabet. This work proves that, on the contrary, the generalization to the r-letter case is possible, thus leading to a O(n$^C$) time complexity algorithm for the case of arbitrary number of letters.