Uniform Random Generation for the Powerset Construction

An algorithm for the uniform random generation of the powerset construction is presented. Given a combinatorial class I, together with a counting procedure and an unranking procedure (or simply a random generation procedure) for I, this algorithm provides counting and unranking (or random generation) procedures for P = powerset(I). For most combi-natorial structures, each random powerset of size n is produced in O(n logn) arithmetic operations in the worst case, after O(n 2) coeecients have been computed. This work is an extension of the algorithms developed in 1, 2], that have been implemented in the Ga a (now combstruct) Maple package 4].