Computing a Diameter-Constrained Minimum Spanning Tree in Parallel

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. 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 NPcomplete, for all values of k; 4 ≤ k ≤ (n − 2). Therefore, one has to depend on heuristics and live with approximate solutions. In this paper, we explore two heuristics for the DCMST problem: First, we present a one-time-treeconstruction algorithm that constructs a DCMST in a modified greedy fashion, employing a heuristic for selecting edges to be added to the tree at each stage of the tree construction. This algorithm is ...

• Type: Conference
• Year: 2000
• Where: CIAC
• Authors: Narsingh Deo, Ayman Abdalla
• Keywords: Algorithms, CIAC 2000, Heuristics, Minimum Spanning Tree, Spanning Trees