Scans as Primitive Parallel Operations
IEEE Transactions on Computers
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Parallel Computations on Reconfigurable Meshes
IEEE Transactions on Computers
Efficient self-simulation algorithms for reconfigurable arrays
Journal of Parallel and Distributed Computing
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Given n elements x0, . . ., xn-1, and given n bits b0, . . . , bn-1, with at least one zero, the segmented scan problem consists in finding the prefixes si = xi ⊗ bis(i-1) mod n, i = 0, . . . , n - 1, where ⊗ is an associative binary operation that can be computed in constant time by a processor. This paper presents: (i) an O(log B) time optimal algorithm for the segmented scan problem on a (2n-1)-node toroidal X-tree, where B is the maximum distance of two successive zeroes in b0, . . . , bn-1; (ii) a novel definition of locally normal algorithms for trees and meshes of trees; (iii) a constant slow-down, optimal, and locally normal simulation algorithm for a class of reconfigurable architectures on the mesh of toroidal X-trees, if the log-time delay model is assumed; (iv) a constant slow-down optimal simulation of locally normal algorithms for meshes of toroidal X-trees on the hypercube.