A bus system whose configuration can be dynamically changed is a reconfigurable bus system. In this paper, on processor arrays with reconfigorable bus systems, two O(1) time algorithms are proposed for computing the transitive closure of an undirected graph. One is designed on a three-dimensional n x n x n processor array with a reconfigurable bus system and the other is designed on a two-dimensional n2 x nz processor array with a recon6gurable bus system, where n is the number of vertices in the graph. Using the O(1) time transitive closure algorithms, we also solve many other graph problems in O(1) time. These problems include recognizing bipartite graphs and finding connected components, articulation points, biconnected components, bridges, and minimum spanning trees in undirected graphs.

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In this paper, a new two-level interconnection network, called a hierarchical folded-hypercube network (HFN, for short), is proposed. The HFN takes folded hypercubes as basic modules which are connected in a complete manner. We investigate the topological properties of the HFN, including the diameter, cost, average distance, embedding, connectivity, container, rc-wide diameter, and node-fault diameter. We show that the HFN can emulate algorithms which are executable on the ring or the mesh-connected computer with the same time complexities in big-0 notation. Moreover, the HFN can embed a folded hypercube having the same number of nodes with constant dilation. We compute the diameter, node connectivity, best container, K-wide diameter, and node-fault diameter of the HFN. We present optimal routing and broadcasting algorithms for the HFN. The semigroup computation and descendascend algorithms can be executed as well on the HFN.

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