Random-tree Diameter and the Diameter-constrained MST

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tree diameter is useful, for example, in determining an upper bound on the expected number of links between two arbitrary documents on the World Wide Web. The DiameterConstrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph G with n nodes and a positive integer k, find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NP-complete, for all values of k; 4 k n - 2). In this paper, we investigate the behavior of the diameter of MST in randomly-weighted complete graphs (in Erd

• Type: Journal
• Year: 2002
• Where: IJCM
• Authors: Ayman Abdalla, Narsingh Deo
• Keywords: Algorithm, IJCM 2002, Spanning Tree, Tree