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On Computing the Subset Graph of a Collection of Sets
, 1995
"... Let a given collection of sets have size N measured by the sum of the cardinalities. Yellin and Jutla presented an algorithm which constructed the partial order induced by the subset relation (a "subset graph") in O(N 2 = log N) operations over a dictionary ADT, and exhibited a collection whose su ..."
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Let a given collection of sets have size N measured by the sum of the cardinalities. Yellin and Jutla presented an algorithm which constructed the partial order induced by the subset relation (a "subset graph") in O(N 2 = log N) operations over a dictionary ADT, and exhibited a collection whose subset graph had \Theta(N 2 = log 2 N) edges. This paper establishes a matching upper bound on the number of edges in a subset graph, shows that the known bound on Yellin and Jutla's algorithm is tight, presents a simple implementation requiring O(1) bitparallel operations per ADT operation, and presents a variant of the algorithm with an implementation requiring O(N 2 = log N) RAM operations. 1 Introduction Yellin and Jutla [9] tackled the following problem. Our interest in it arose from the application studied in [6], but we feel the problem is a fundamental one, likely to arise in many contexts. Given is a collection F = fS 1 ; : : : ; S k g, where each S i is a set over the same d...