Scans as Primitive Parallel Operations

AbstmctIn most parallel random access machine (PRAM) models, memory references are assumed to take unit time. In practice, and in theory, certain scan operations, also known as prefix computations, can execute in no more time than these parallel memory references. This paper outlines an extensive study of the effect of including, in the PRAM models, such scan operations as unit-time primitives. The study concludes that the primitives improve the asymptotic running time of many algorithms by an O(log n) factor greatly simplify the description of many algorithms, and are significantly easier to implement than memory references. We therefore argue that the algorithm designer should feel free to use these operations as if they were as cheap as a memory reference. This paper describes five algorithms that clearly illustrate how the scan primitives can be used in algorithm design: a mdixsort algorithm, a quicksort algorithm, a minimum-spanning-trae algorithm, a line-dmwing algorithm, and a merging algorithm. These all run on an EREW PRAM with the addition of two scan primitives, and are either simpler or more efficient than their pure PRAM counterparts. The scan primitives have been implemented in microcode on the Connection Machine System, are available in PARIS (the parallel instruction set of the machine), and are used in a large number of applications. All five algorithms have been tested, and the radix sort is the currently supported sorting algorithm for the Connection Machine.