Average-case communication-optimal parallel parenthesis matching

Abstract

We provide the first non-trivial lower bound, p-3/p·n/p, wherep is the number of the processors and n is the data size, on the average-case communication volume, σ, required to solve the parenthesis matching problem and present a parallel algorithm that takes linear (optimal) computation time and optimal expected message volume, σ + p. The kernel of the algorithm is to solve the all nearest smaller values problem. Provided n/p = Ω(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 (n/p + p) in the worst case and p in the average case, assuming the input instances are uniformly distributed. © Springer-Verlag Berlin Heidelberg 2002.