On Asymptotically Optimal Approach for Finding of the Minimum Total Weight of Edge-Disjoint Spanning Trees with a Given Diameter

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Abstract

We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity O(n2), where n is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution.

About the authors

E. Kh. Gimadi

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: gimadi@math.nsc.ru
Novosibirsk, Russia

A. A. Shtepa

Novosibirsk State University

Author for correspondence.
Email: shoomath@gmail.com
Novosibirsk, Russia

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