Parallel minimum spanning forest algorithms on the star and pancake interconnection networks

Abstract

Parallel algorithms are described for computing minimum spanning forests in both sparse and dense weighted graphs. The algorithms are designed to run on the star and pancake interconnection networks. Their time complexities match those of the equivalent hypercube algorithms, thanks mainly to a novel routing scheme. The latter unifies data routing on the star and pancake networks, and makes these networks as powerful as the hypercube when solving a host of problems, and it allows a certain class of algorithms designed for the hypercube to be implemented directly on the star and pancake networks without time loss. These results take added importance when one recalls the many attractive properties that the star and pancake networks possess by comparison with the hypercube, in particular their smaller degree and diameter.