Performance of parallel spanning tree algorithms on linear arrays of transputers and Unix systems

This paper presents empirical performance of parallel algorithms for computing a spanning tree (SPT) and a minimum spanning tree (MST) of connected graphs on the Transputer and Unix systems, where processors are configured as a one-dimensional array. The parallel MST algorithm uses a weight matrix data structure; and three implementations of the SPT algorithm are presented with unordered edge-list, linked adjacency list and adjacency matrix as data structures. The experiments are conducted with a wide range of random graphs, generated for various edge-densities (d) for a given number (n) of vertices. The edge-density is varied between 0.1 and 0.9, and the maximum number of vertices (or edges) considered are 300 (or 40000) and 500 (or 110000) for transputer and Unix systems, respectively. A maximum speed-up of 2.98 is achieved on the transputer network of eight processors, and that for the Unix system is 3.0 with four processors