Managing a Parallel Heap Efficiently

Abstract

We design a cost-optimal algorithm for managing a parallel heap on an exclusive-read and exclusive-write (EREW), parallel random access machine (PRAM) model. This is an improvement in space and time over the one recently proposed by Deo and Prasad [4]. Our approach efficiently employs p processors in the range 1≤ p≤ n, where n is the maximum number of items in a parallel heap. It is assumed that a delete-think-insert cycle is repeatedly performed, and each processor requires an arbitrary but the same amount of time (called the think time) for processing an item which in turn generates at most α (a constant) new items. The time required for deleting p items of the highest priority from the parallel heap is O(1), while that for inserting at most αp new items is O(log n). With or without incorporating the think time, the speedup of our algorithm is proved to be linear, i.e. O(p). Using a global, working data structure for each level of the heap, it is shown that the additional memory space required for our parallel heap is much less than that for the existing one [4]. Furthermore, the proposed algorithm retains the strict priority ordering of a sequential heap.