Parallel Algorithms for Generating Subsets and Set Partitions

We present adaptive and cost-optimal parallel algorithms for generating 1) all subsets of the set {1,...,n}, 2) all limited size subsets (each subset has at most m elements for a given m), and 3) all partitions of the set. The algorithms are based on a simple model of parallel computation which assumes the existence of k individual processors operating synchronously without need to communicate among themselves. Parallel ranking and unranking procedures for each case are also presented. Applications of the parallel subset generation algorithm to subset-sum, knapsack and base-enumeration problems are subsequently presented.

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