Parallel Min-max-pair Heap

Abstract

Priority deques allow, in addition to the priorityqueue operations of inserting an element and deleting the largest element, the deletion of the smallest element. Data structures like min-max heap, deap, minmax-pair heap, and interval heap, described in the literature, for implementing priority deques achieve only O(1ogn)-parallelism, where n is the number of elements. To alleviate this bottleneck, we present the parallel min-max-pair heap, a new parallel data structure for priority deques, which achieves a pfold parallelism with p processors for all p 5 n. First, we describe how it supports deletion of p largest elements, deletion of p smallest elements, and insertion of p elements in O(log n logp) time using p processors on the exclusive-read exclusive-write (EREW) parallel random-access machine (PRAM). Then, to obtain cost-optimal parallel algorithms, we show that the operations can be pipelined on this structure and that p operations can be handled in O(1ogn) time with p processors.