Prefix codes: Equiprobable words, unequal letter costs

We consider the following Variant of Huffman coding in which the costs of the letters, rather than the probabilities of the words, are nonuniform: `'Given an alphabet of r letters of nonuniform length, find a minimum-average-length prefix-free set of n codewords over the alphabet''; equivalently, `'Find an optimal r-ary search tree with n leaves, where each leaf is accessed with equal probability but the cost to descend from a parent to its ith child depends on i.'' We show new structural properties of such codes, leading to an O(nlog(2) r)-time algorithm for finding them, This new algorithm is simpler and faster than the best previously known O(nr min{logn, r})-time algorithm, due to Perl, Garey, and Even [J. Assoc, Comput. Mach., 22 (1975), pp. 202-214]