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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 𝒪(n2) (𝒪(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., 19: 472–497, 2001