A Paradigm for the Design of Parallel Algorithms with Applications

This paper proposes a model or paradigm for the development of parallel algorithms, gives an example of the proposed paradigm, and displays algorithms developed by application of the technique. The algorithm for the merge of two ordered lists developed through application of this technique is thought to be original. The paradigm proposed is to create composite unit operations which combine data movement between data structures with a conventional operation such as compare or add. The composite operation constructed for this study is based upon partitioning the data elements into two linear lists. Exchange of data between adjacent elements in each list are then combined with compares and adds to complete the composite operations. This composite operation can be implemented on at least the following computational architectures. 1) SIMD with all processors sharing a common memory. 2) SIMD with local memories and a linear interconnection (circular pipeline or ring network of processors). 3) Vector processor with common memory, such as a CDC CYBER 205 or a Cray Research CRAY-1. The algorithms developed all have the property of linear speed-up with the number of processing elements. The algorithms developed include sorting, merging, selection among sets, set interconnection, set difference, subset testing, and string matching.