An efficient algorithm for constructing nearly optimal prefix codes

Kurt Mehlhorn

Abstract: A new algorithm is presented for constructing nearly optimal prefix codes in the case of unequal letter costs and unequal probabilities. A bound on the maximal deviation from the optimum is derived and numerical examples are given. The algorithm has running time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(t \cdot n)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> is the number of letters and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is the number of probabilities.