Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
A bridging model for parallel computation
Communications of the ACM
Parallel computation: models and methods
Parallel computation: models and methods
Communication efficient BSP algorithm for all nearest smaller values problem
Journal of Parallel and Distributed Computing
Searching, Merging, and Sorting in Parallel Computation
IEEE Transactions on Computers
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We provide the first non-trivial lower bound, p-3p.np, where p is the number of the processors and n is the data size, on the average-case communication volume, @s, required to solve the parenthesis matching problem, assuming problem instances are uniformly distributed, and present a parallel algorithm that takes linear (optimal) computation time and optimal expected message volume, @s+p. The kernel of the algorithm is to solve the all nearest smaller values problem. Provided np=@W(p), we present an algorithm that achieves optimal sequential computation time and uses only a constant number of communication phases, with the message volume in each phase bounded above by (np+p) in the worst case and p in the average case. Experiments have been performed on two clusters: an SGI Intel Linux Cluster and a Sun cluster of workstations, both showing low communication overhead and good speedups.