The Complexity of Finding Replicas Using Equality Tests

We prove (for fixed k) that at least 1 k−1 (n 2 ) − O(n) equality tests and no more than 2 k (n 2 )+O(n) equality tests are needed in the worst case to determine whether a given set of n elements contains a subset of k identical elements. The upper bound is an improvement by a factor 2 compared to known results. We give tighter bounds for k = 3.

• Type: Conference
• Year: 1993
• Where: MFCS
• Authors: Gudmund Skovbjerg Frandsen, Peter Bro Miltersen, Sven Skyum
• Keywords: Equality Tests, Identical Elements, MFCS 1993, Theoretical Computer Science, Worst Case