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<p><b>Abstract</b>—The parallel computation model upon which the proposed algorithms are based is the hyper-bus broadcast network. The hyper-bus broadcast network consists of processors which are connected by global buses only. Based on such an improved architecture, we first design two <it>O</it>(1) time basic operations for finding the maximum and minimum of <it>N</it> numbers each of size <it>O</it>(log <it>N</it>)-bit and computing the matrix multiplication operation of two <it>N</it>×<it>N</it> matrices, respectively. Then, based on these two basic operations, three of the most important instances in the algebraic path problem, the connectivity problem, and several related problems are all solved in <it>O</it>(log <it>N</it>) time. These include the all-pair shortest paths, the minimum-weight spanning tree, the transitive closure, the connected component, the biconnected component, the articulation point, and the bridge problems, either in an undirected or a directed graph, respectively.</p>
Hyper-bus broadcast network, parallel algorithm, graph theory, matrix multiplication operation, algebraic path problem, connectivity, all-pair shortest paths, minimum-weight spanning tree, transitive closure, connected component, biconnected component, articulation point, bridge.
Tzong-Wann Kao, Shung-Shing Lee, Shi-Jinn Horng, Shun-Shan Tsai, Horng-Ren Tsai, "Solving An Algebraic Path Problem and Some Related Graph Problems on a Hyper-Bus Broadcast Network", IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 1226-1235, December 1997, doi:10.1109/71.640014
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