Asymptotically Optimal Approach to a Given Diameter Undirected MST Problem on Random Input Data

We give an approximation deterministic algorithm for solving the Random Undirected MST with given diameter on n-vertex complete undirected graph. The problem is NP-hard. Algorithm has a quadratic time complexity. A probabilistic analysis was performed under conditions that edge weights of given graph are identically independent uniformly distributed random variables on an interval with positive ends. Sufficient conditions of asymptotic optimality are presented.