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<p>The transitive closure problem in O(1) time is solved by a new method that is far different from the conventional solution method. On processor arrays with reconfigurable 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*n*n processor array with a reconfigurable bus system, and the other is designed on a two-dimensional n/sup 2/*n/sup 2/ processor array with a reconfigurable bus system, where n is the number ofvertices in the graph. Using the O(1) time transitive closure algorithms, many other graph problems are solved 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.</p>
Index Termstransitive closure; related graph problems; processor arrays; reconfigurable bus systems; transitive closure; undirected graph; graph problems; bipartite graphs; connected components; articulation points; biconnected components; bridges; minimum spanning trees; graph theory; parallel algorithms
G.H. Chen, B.F. Wang, "Constant Time Algorithms for the Transitive Closure and Some Related Graph Problems on Processor Arrays with Reconfigurable Bus Systems", IEEE Transactions on Parallel & Distributed Systems, vol. 1, no. , pp. 500-507, October 1990, doi:10.1109/71.80177
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