Optimal Segmented Scan and Simulation of Reconfigurable Architectures on Fixed Connection Networks

Abstract

Given n elements x₀, . . . , x_n-1, and given n bits b₀, … , b_n-1, with at least one zero, the segmented scan problem consists infinding the prefixes s_i = x_i ⊗ b_is(_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 (2_n-1)-node toroidal X-tree, where B is the maximum distance of two successive zeroes in b₀, . . . , b_n-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.

This work has been supported by grants from the University of Trento and the Provincia Autonoma di Trento.