PRAM processor allocation: a hidden bottleneck in sublogarithmic algorithms

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 Ω(log P) lower bound, even when the number of tasks is O(√P ). The second, called assignment from leaders, has faster solutions. A constant-time solution for O(√P) tasks is known; it is generalized to O(P^1-1k/) 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