Optimal expression evaluation for data parallel architectures

Optimal Expression Evaluation for Data Parallel Architectures

A data parallel machine represents an array or other composite data structure by allocating one processor (at least conceptually) per data item. A pointwise operation can be performed between two such arrays in unit time, provided their corresponding elements are allocated in the same processors. If the arrays are not aligned in this fashion, the cost of moving one or both of them is part of th...

Optimal Static 2-Dimensional Screen Subdivision for Parallel Rasterization Architectures

Designers of computer graphics hardware have used increasing device counts available from IC manufacturers to increase parallelism using techniques such as putting a longer pipeline of data path elements on integrated circuits. or developing designs which use an array of processors. Pixel-Planes 1-5 and PixelFIow l are examples of architectures which use an array of pixel processors for rasteri...

Optimal Algorithms for Parallel Polynomial Evaluation

An Optimal Parallel Algorithm for Formula Evaluation

A new approach to Buss’s NC algorithm [Bus87] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC over AC reductions. This approach is then used to solve the more general problem of evaluating arithmetic formulas using arithmetic circuits.

Optimal Parallel Evaluation ofMatrix Product

We consider the problem of parallel evaluation of the expression We demonstrate, using an example, that the optimal order for sequential evaluation is not necessarily optimal for parallel evaluation. There are two diierent levels of parallelism that we shall consider. The rst is that of evaluating diierent products in parallel and the second is that of evaluating a single product using several ...