Parallelism and locality in priority queues

We explore two ways of incorporating parallelism into priority queues. The rst is to speed up the execution of individual priority operations so that they can be performed one operation per time step, unlike sequential implementations which require O(log N) time steps per operation for an N element heap. We give an optimal parallel implementation that uses a linear array of O(log N) processors. Second, we consider parallel operations on the priority queue. We show that using a d-dimensional array (constant d) of P processors we can insert or delete the smallest P elements from a heap in time O(P 1=d log 1?1=d P), where the number of elements in the heap is assumed to be polynomial in P. We also show a matching lower bound, based on communication complexity arguments, for a range of determin-istic implementations. Finally, using randomization, we show that the time can be reduced to the optimal O(P 1=d) time with high probability.