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In this paper we present deterministic algorithms for integer sorting and on-line packet routing on arrays with reconfigurable optical buses. The main objective is to identify the mechanisms specific to this type of architectures that allow us to build efficient integer sorting, partial permutation routing and /i-relations algorithms. The consequences of these results on the PRAM simulation complexity are also investigated.

A general model for determining the computational efficiency of a particular class of electro-optical systems is described. The model is an abstraction of parallel systems that use digital electronic processors and optical pipelined buses for communication. Minimum requirements in terms of area (volume for three-dimensional structures) and time necessary in order to solve a problem are obtained. Different applications are investigated, and a matching area-time upper bound is given for the barrel-shift problem, simulated on an array with reconfigurable optical pipelined buses. The types of problems for which these lower bounds seem to be realistic are described.

The Euclidean Distance Transform is an important computational tool for the processing of binary images, with applications in many areas such as computer vision, pattern recognition and robotics. We investigate the properties of this transform and describe an O(n2) time optimal sequential algorithm. A deterministic EREW-PRAM parallel algorithm which runs in O( log n) time using O(n2) processors and O(n2) space is also derived. Further, a cost optimal randomized parallel algorithm which runs within the same time bounds with high probability, is given.

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