Information carefull worstcase DecreaseKey heaps with simple nonMeld variant

TL;DR

This paper investigates priority queues with DecreaseKey operations, inspired by Strict Fibonacci Heaps, aiming to develop variants that optimize information retention and comparison costs in worst-case scenarios.

Contribution

It introduces new structural variants of DecreaseKey heaps that focus on minimizing information loss and maximizing comparison efficiency, inspired by prior theoretical principles.

Findings

Proposes variants with improved worst-case performance

Analyzes information retention during violation reduction

Aligns with superexpensive comparison principles

Abstract

We analyze priority queues including DecreaseKey method in its interface. The paper is inspired by Strict Fibonacci Heaps [2], where G. S. Brodal, G. Lagogiannis, and R. E. Tarjan implemented the heap with DecreaseKey and Meld interface in assymptotically optimal worst case times (based on key comparisons). At the end of the paper there are mentioned possible variants of other structural properties an violations than they have used in the analysis. In the main variant a lot of information is wasted during violation reduction steps. Our goal is to concentrate on other variants and to invent natural strategy not losing that much in the information value. In other words we try to choose among them one which corresponds to superexpensive comparision principle as much as possible. The principle was described in [5] of myself, but after publication I have found these ideas in [4] of H. Kaplan, R. E. Tarjan, and U. Zwick.