# Padovan heaps

## TL;DR

This paper introduces Padovan heaps, a new type of Fibonacci-family priority queue that uses a superexpensive comparison principle to achieve narrower heaps while maintaining optimal amortized bounds.

## Contribution

It presents the design and analysis of Padovan heaps, achieving narrower heap structures inspired by Violation heaps and superexpensive comparison principles.

## Key findings

- Achieves the same amortized bounds as Fibonacci heaps
- Heaps are narrower than previous Fibonacci-family heaps
- Introduces superexpensive comparison principle in heap design

## Abstract

We analyze priority queues of Fibonacci family. The paper is inspired by Violation heap [1], where A. Elmasry saves one pointer in representation of Fibonacci heap nodes while achieving the same amortized bounds as Fibonacci heaps [2] of M. L. Fredman and R. E. Tarjan. Unfortunately author forces the heaps to be wide, what goes against optimal heap principles. Our goal is to achieve the same result, but with much narrower heaps. We follow the principle of superexpensive comparison so we try to remember results of all comparisons and never compare elements that cannot be minimal. We delay comparisons as long as possible. Actually I have always want to share superexpensive comparison principle ideas, discovery of Padovan heaps allowed me to do so. Of course saving one pointer is not that big goal, but I hope the presented reasoning and amortized analysis of the resulting heaps is worth a publication.