A generic approach for the unranking of labeled combinatorial classes

In this article, we design and analyze algorithms that solve the unranking problem (i.e., generating a combinatorial structure of size, n given its rank) for a large collection of labeled combinatorial classes, those that can be built using operators like unions (+), products ( ), sequences, sets, cycles, and substitutions. We also analyze the performance of these algorithms and show that the worst-case is n2 ( n log n if the so-called boustrophedonic order is used), and provide an algebra for the analysis of the average performance and higher-order moments together with a few examples of its application. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 00, 1–26, 2001