The Complexity of Identifying Large Equivalence Classes

  • Peter G. Binderup
  • Gudmund Skovbjerg Frandsen
  • Peter Bro Miltersen
  • Sven Skyum


We prove that at least (3k−4) / k(2k−3) n(n-1)/2 − O(k) equivalence tests and no
more than 2/k n(n-1)/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] .

How to Cite
Binderup, P., Frandsen, G., Miltersen, P., & Skyum, S. (1998). The Complexity of Identifying Large Equivalence Classes. BRICS Report Series, 5(34).