Parallel Min-max-pair Heap

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.