PRAM processor allocation: a hidden bottleneck in sublogarithmic algorithms

Abstract

The problem of dynamic processor allocation in PRAMs (programmable random-access memories) is discussed, and differentiated from that of static allocation. The version of the PRAM considered, also called the CREW model is a parallel computer with global memory accessible in unit time; it allows concurrent reads, but requires exclusive writes. Two dynamic processor allocation problems for P processors are distinguished. One, called assignment from numbers, has an Omega (log P) lower bound, even when the number of tasks is O( square root P). The second, called assignment from leaders, has faster solutions. A constant-time solution for O( square root P) tasks is known; it is generalized to O(P/sup 1-1/k/) tasks in time O(k). Handling O(P) tasks requires a different approach and an algorithm that runs in time O(log log P) is proposed which is asymptotically optimal within a constant factor. The implications of these two versions of dynamic allocation on sublogarithmic merge algorithms are discussed. >