Two new methods for constructing double-ended priority queues from priority queues

Abstract

We introduce two data-structural transformations to construct doubleended priority queues from priority queues. To apply our transformations the priority queues exploited must support the extraction of an unspecified element, in addition to the standard priority-queue operations. With the first transformation we obtain a double-ended priority queue which guarantees the worst-case cost of O(1) for find-min, find-max, insert, extract; and the worst-case cost of O(lg n) with at most lg n + O(1) element comparisons for delete. With the second transformation we get a meldable double-ended priority queue which guarantees the worst-case cost of O(1) for find-min, find-max, insert, extract; the worst-case cost of O(lg n) with at most lg n + O(lg lg n) element comparisons for delete; and the worst-case cost of O(min {lg m, lg n}) for meld. Here, m and n denote the number of elements stored in the data structures prior to the operation in question.

Regular numeral systems for data structures

“…Even though Borrow is a non-standard operation, its importance has been demonstrated in several papers (see, for example, [14,19,20,25,36]).…”

A Survey on Priority Queues

“…General techniques to convert single ended priority queues into double-ended priority queues were presented by Chong and Sahni [32] and Elmasry et al [57]. Alternative implementations of implicit double-ended queues include [106,26,37,99,6].…”

Bipartite binomial heaps

“…Of these operations, Borrow is non-standard, but its importance has been demonstrated in several earlier papers, see e.g. [2,5,8,9,15]. Most notably, in [9], we used several (single-ended) priority heaps to implement a double-ended priority heap.…”

“…[2,5,8,9,15]. Most notably, in [9], we used several (single-ended) priority heaps to implement a double-ended priority heap. When moving elements from one priority heap to another, efficient Borrow and Insert operations were essential.…”