On Computing the Subset Graph of a Collection of Sets

Paul Pritchard
1999 Journal of Algorithms  
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 (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,
more » ... s a simple implementation requiring O(1) bit-parallel operations per ADT operation, and presents a variant of the algorithm with an implementation requiring O(N 2 = log N) RAM operations.
doi:10.1006/jagm.1999.1032 fatcat:qngjbkidifas7dzn3i6e3l4diq