Abstract
A systolic algorithm is described for generating, in lexicographically ascending order, all combinations of m objects chosen from an arbitrary set of n elements. The algorithm is designed to be executed on a linear array of m processors, each having constant size memory (except processor m, which has O(n) memory), and each being responsible for producing one element of a given combination. There is a constant delay per combination, leading to an O (C(m, n)) time solution, where C(m, n) is the total number of combinations. The algorithm is cost-optimal (assuming the time to output the combinations is counted), and does not deal with very large integers.
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