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The algebraic path problem is a general description of a class of problems, including some important graph problems such as transitive closure, all pairs shortest paths, minimum spanning tree, etc. In this work, the algebraic path problem is solved on a processor array with a reconfigurable bus system. The proposed algorithms are based on repeated matrix multiplications. The multiplication of two n*n matrices takes O(log n) time in the worst case, but, for some special cases, O(1) time is possible. It is shown that three instances of the algebraic path problem, transitive closure, all pairs shortest paths, and minimum spanning tree, can be solved in O(log n) time, which is as fast as on the CRCW PRAM.
Index Termsparallel computation; algebraic path problem; graph problems; transitive closure; all pairsshortest paths; minimum spanning tree; processor array; reconfigurable bus system;repeated matrix multiplications; CRCW PRAM; computational complexity; graph theory;parallel algorithms

G. Chen, B. Wang and C. Lu, "On the Parallel Computation of the Algebraic Path Problem," in IEEE Transactions on Parallel & Distributed Systems, vol. 3, no. , pp. 251-256, 1992.
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