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Research and Advances

Computing connected components on parallel computers

We present a parallel algorithm which uses n2 processors to find the connected components of an undirected graph with n vertices in time O(log2n). An O(log2n) time bound also can be achieved using only n⌈n/⌈log2n⌉⌉ processors. The algorithm can be used to find the transitive closure of a symmetric Boolean matrix. We assume that the processors have access to a common memory. Simultaneous access to the same location is permitted for fetch instructions but not for store instructions.
Research and Advances

Fast parallel sorting algorithms

A parallel bucket-sort algorithm is presented that requires time O(log n) and the use of n processors. The algorithm makes use of a technique that requires more space than the product of processors and time. A realistic model is used in which no memory contention is permitted. A procedure is also presented to sort n numbers in time O(k log n) using n1+1/k processors, for k an arbitrary integer. The model of computation for this procedure permits simultaneous fetches from the same memory location.

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