On the Single-Operation Worst-Case Time Complexity on the Disjoint Set Union Problem

We give an algorithm for the disjoint set union problem, within the class of algorithms defined by Tarjan, which has O(log n/loglog n) single-operation time complexity in the worst-case. Also we define a class of algorithms for the disjoint set union problem, which includes the class of algorithms defined by Tarjan. We prove that any algorithm from this class has at least ω(log n/loglog n) single-operation time complexity in the worst-case.