Huffman coding with unequal letter costs

(MATH) In the standard Huffman coding problem, one is given a set of words and for each word a positive frequency. The goal is to encode each word w as a codeword c(w) over a given alphabet. The encoding must be prefix free (no codeword is a prefix of any other) and should minimize the weighted average codeword size Σ w freq w , | c(w) |. The problem has a well-known polynomial-time algorithm due to Huffman [15].Here we consider the generalization in which the letters of the encoding alphabet may have non-uniform lengths. The goal is to minimize the weighted average codeword length Σ w freq ( w ) cost( c ( w )), where cost s is the sum of the (possibly non-uniform) lengths of the letters in s . Despite much previous work, the problem is not known to be NP-hard, nor was it previously known to have a polynomial-time approximation algorithm. Here we describe a polynomial-time approximation scheme (PTAS) for the problem.

Authors

• Mordecai J. Golin
• Claire Mathieu
• Neal E. Young

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