Optimal processor-time tradeoffs on massively parallel memory-based architectures

Processor-time-optimal algorithms are presented for several image and graph problems on a parallel architecture that combines an orthogonally accessed memory with a linear array structure. The organization has p processors and a memory of size Θ(n²) locations. The number of processors p can vary over a wide range while providing processor-time-optimal algorithms for sorting and for several problems from graph theory, computational geometry, and image analysis. Sorting and geometric problems can be solved in O((n² /p) log n+n) time, which is optimal for p in the range [1, n log n]. Graph and image problems can be solved in O(n²/p+ n^1/2) time, which is optimal for p in the range [1, n^3/2]. The algorithms implemented on the proposed architecture have processor-time products superior to those of the mesh and pyramid computer algorithms