Semigroup computation and its applications on mesh-connected computers with hyperbus broadcasting

Let ⊕ be an associative operation on a domain D. The semigroup problem is to compute a₀⊕a₁⊕...a_N-1, where a_i ∈D, for 0⩽i<N. The algorithm described here runs on SIMD mesh-connected computers with hyperbus broadcasting using p processors in time O(N/p+logp), where p⩽N. It as shown optimal when p=N and optimal speedup when p log p=N. Based on the proposed semigroup algorithm, other applications such as matrix multiplication, all-pair shortest path, shortest path spanning tree, topological sorting and connected component problems can be also solved in the order of logarithmic time using N³ processors