A rearrangement step with potential uses in priority queues

TL;DR

The paper introduces a new rearrangement primitive for link-based, heap-ordered priority queues that maintains a logarithmic number of trees and is amortized constant time, enhancing efficiency in such data structures.

Contribution

It presents a novel rearrangement step for heap-ordered binary trees that improves control over the number of trees and operates with amortized constant complexity.

Findings

Maintains logarithmic number of trees in priority queues.

Operates with amortized constant complexity.

Applicable to link-based heap-ordered structures.

Abstract

Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive designed for link-based, heap-ordered priority queues in the comparison model, such as those similar to Fibonacci heaps or binomial heaps. In its most basic form, the primitive rearranges a collection of heap-ordered perfect binary trees. Doing so offers a data structure control on the number of trees involved in such a collection, in particular keeping this number logarithmic in the number of elements. The rearrangement step is free from an amortized complexity standpoint (using an appropriate potential function).