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<p>Parallel algorithms for several important combinatorial problems such as the all nearest smaller values problem, triangulating a monotone polygon, and line packing are presented. These algorithms achieve linear speedups on the pipelined hypercube, and provably optimal speedups on the shuffle-exchange and the cube-connected-cycles for any number p of processors satisfying 1>or=p>or=n/((log/sup 3/n)(loglog n)/sup 2/), where n is the input size. The lower bound results are established under no restriction on how the input is mapped into the local memories of the different processors.</p>
Index Termsparallel algorithms; pipelined hypercube; combinatorial problems; monotone polygon; line packing; shuffle-exchange; cube-connected-cycles; combinatorial mathematics; computational geometry; parallel algorithms; pipeline processing

J. JáJá and K. Ryu, "Optimal Algorithms on the Pipelined Hypercube and Related Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 582-591, 1993.
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