Derivation of systolic algorithms for the algebraic path problem by recurrence transformations

• Published in: Parallel computing Vol. 26; no. 11; pp. 1429 - 1445
• Main Authors: Djamégni, Clémentin Tayou, Quinton, Patrice, Rajopadhye, Sanjay, Risset, Tanguy
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2000
• Subjects: Algebraic path problem; Dependence graph; Systolic architectures; Uniform recurrence equations; Uniform recurrence equations; Algebraic path problem; Dependence graph; Systolic architectures
• ISSN: 0167-8191; 1872-7336
• DOI: 10.1016/S0167-8191(00)00039-9

In this paper, we are interested in solving the algebraic path problem (APP) on regular arrays. We first unify previous contributions with recurrence transformations. Then, we propose a new localization technique without long-range communication which leads to a piecewise affine scheduling of 4 n+ Θ(1) steps, where n is the size of the problem. The derivation of a locally connected space-time minimal solution with respect to the new scheduling constitutes the second contribution of the paper. This new design requires n 2/3+ Θ( n) elementary processors and solves the problem in 4 n+ Θ(1) steps, and this includes loading and unloading time. This is an improvement over the best previously known bounds.