Abstract
Abstract In this paper we consider the worst-case adaptive complexity of the search problem (S, F ) , where F is also the set of independent sets of a matroid over S. We give a formula for the number of questions needed and an algorithm to find the optimal search algorithm for any matroid. This algorithm uses only O(|S|3) steps (i.e. questions to the independence oracle). This is also the length of Edmonds’ partitioning algorithm for matroids, which does not seem to be avoidable.
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