The Complexity of Identifying Large Equivalence Classes

Authors:
Sven Skyum;Gudmund S. Frandsen;Peter Bro Miltersen;Peter G. Binderup
Affiliations:
(Correspd.) BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus.;BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus.;BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus.;BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus.
Venue:
Fundamenta Informaticae
Year:
1999

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Abstract

We prove that at least 3k−4/k(2k−3)(n/2) - O(k)equivalence tests and no more than 2/k (n/2) + O(n) equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighter bounds. Finally, for k n/2 we prove that it is necessary and it suffices to make 2n − k − 1 equivalence tests which generalizes a known result for k = [n+1/2].