Fast DecreaseKey Heaps with worst-case variants

TL;DR

This paper presents a simplified and readable version of a heap data structure with efficient worst-case DecreaseKey operations, improving understanding without introducing entirely new structures.

Contribution

It offers an accessible description of a heap with worst-case optimal DecreaseKey, distinct from prior complex implementations, focusing on clarity and ease of understanding.

Findings

Heap operations have guaranteed worst-case asymptotic times.

The proposed structure simplifies understanding of DecreaseKey heaps.

The paper does not introduce a new data structure but clarifies existing concepts.

Abstract

In the paper "Fast Fibonacci heaps with worst case extensions", we have described heaps with both Meld-DecreaseKey and DecreaseKey interfaces, allowing operations with guaranteed worst-case asymptotically optimal times. The paper was intended to concentrate on the DecreaseKey interface, but it could be hard to separate the two described data structures without careful reading. The current paper's goal is not to invent a novel data structure, but to describe a rather easy DecreaseKey version in a hopefully readable form. The paper is intended not to require reference to other papers.