PERFORMANCE OF PARALLEL SPANNING TREE ALGORITHMS ON LINEAR ARRAYS OF TRANSPUTERS AND UNIX SYSTEMS

This paper presents empirical performance of parallel algorithms for connected graphs on the transputer and Unix systems, where processes are configured as a one-dimensional array. We conduct experiments for implementing (i) spanning tree algorithm (SPT-list) with unordered list of edges as input, (ii) SPT algorithm with adjacency matrix, (iii) minimum spanning tree algorithm (MST) with weight matrix as input, and (iv) SPT algorithm derived from MST algorithm by assigning each edge-weight equal to 1. The empirical study is performed with a wide range of random graphs, generated for various (uniformly distributed) edge-densities (d) for a given number (n) of vertices. We plot curves for resulting speedups as functions of n, d, and p. The edge-density d is varied between 0.1 and 0.9; maximum number of vertices (or edges) considered are 300 (or 40 000) and 500 (or 110 000) for transputer and Unix systems, respectively; and the number of processors p varies from 1 through 8 in the transputer system while 1 through 4 in the Unix system. A maximum speedup of 2.98 is obtained on transputers, and that for the Unix system is 3.0. We observe that the speedups of all algorithms vary with increasing number of vertices or edge-density. However, employing more processing units in an algorithm does not necessarily enhance its speedup because of additional communication overhead.