On Time Optimal Implementation of Uniform Recurrences onto Array Processors via Quadratic Programming

Authors:
Karl-Heinz Zimmermann;Wolfgang Achtziger
Affiliations:
Department of Electrical and Computer Engineering, Technical University of Hamburg-Harburg, Martin-Leuschel-Ring 16, D-21071 Hamburg, Germany;Institute of Applied Mathematics, University of Erlangen-Nuremberg, Martensstraße 3, D-91058 Erlangen, Germany
Venue:
Journal of VLSI Signal Processing Systems
Year:
1998

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Abstract

Many important algorithms can be described byn-dimensional uniform recurrences. The computations are thenindexed by integral vectors of length n and the datadependencies between computations can be described by thedifference vector of the corresponding indexes which areindependent of the indexes. This paper addresses the followingoptimization problem: Given an n-dimensional uniformrecurrence whose computation indexes are mapped by a linearfunction onto the processors of an array processor embedded ink-space (1≤ k ≤ n). Find an optimal linear functionfor the computation indexes. We study a continuousapproximation of this problem by passing from linear toquasi-linear timing functions. The resultant problemformulation is then a quadratic programming problem which can besolved by standard algorithms for quadratic or general nonlinearoptimization problems. We demonstrate the effectiveness of ourapproach by several nontrivial test examples.