Worst-Case Optimal Priority Queues via Extended Regular Counters

TL;DR

This paper introduces a simplified, more efficient variant of worst-case optimal priority queues using extended regular counters, achieving similar asymptotic bounds with smaller constants and easier implementation.

Contribution

A new priority queue data structure based on extended regular counters that simplifies the design and improves constants while maintaining worst-case optimal bounds.

Findings

Achieves the same asymptotic bounds as Brodal's original structure.

Simpler design with smaller constants in time and space bounds.

Pointer-machine implementation with $O( ext{log log } n)$ worst-case time for certain operations.

Abstract

We consider the classical problem of representing a collection of priority queues under the operations \Findmin{}, \Insert{}, \Decrease{}, \Meld{}, \Delete{}, and \Deletemin{}. In the comparison-based model, if the first four operations are to be supported in constant time, the last two operations must take at least logarithmic time. Brodal showed that his worst-case efficient priority queues achieve these worst-case bounds. Unfortunately, this data structure is involved and the time bounds hide large constants. We describe a new variant of the worst-case efficient priority queues that relies on extended regular counters and provides the same asymptotic time and space bounds as the original. Due to the conceptual separation of the operations on regular counters and all other operations, our data structure is simpler and easier to describe and understand. Also, the constants in the time and space bounds are smaller. In addition, we give an implementation of our structure on a pointer machine. For our pointer-machine implementation, \Decrease{} and \Meld{} are asymptotically slower and require $O(\lg\lg{n})$ worst-case time, where $n$ denotes the number of elements stored in the resulting priority queue.