Optimal Algorithms on the Pipelined Hypercube and Related Networks

Joseph F. JáJá, Kwan Woo Ryu

Abstract: 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.<