Abstract
We consider the problem of finding the minimal and maximal sets in a family F of sets, i.e. a collection of subsets of some domain. For a family of sets of size N we give an algorithm which finds these extremal sets in expected time O( N 2/log N), and worst case time O( N 2/√log N). All previous algorithms had worst case complexity of ω( N 2). We also present a simple algorithm for dynamically recomputing the minimal and maximal sets as elements are inserted to and deleted from the subsets. This algorithm has a worst case bound of O( N) per update, and this bound is tight.
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