Priority Queue Based on Multilevel Prefix Tree

TL;DR

This paper introduces PTrie, a priority queue structure based on a multilevel prefix tree that achieves efficient operations with a time complexity depending on data size and a matching parameter K.

Contribution

The paper presents PTrie, a novel priority queue structure combining prefix trees, doubly linked lists, and queues, with optimized time complexity for core operations.

Findings

Operations have a time complexity of O(M/K + K)

Structure size depends linearly on the number and size of elements

PTrie outperforms traditional priority queues in efficiency

Abstract

Tree structures are very often used data structures. Among ordered types of trees there are many variants whose basic operations such as insert, delete, search, delete-min are characterized by logarithmic time complexity. In the article I am going to present the structure whose time complexity for each of the above operations is $O(\frac{M}{K} + K)$, where M is the size of data type and K is constant properly matching the size of data type. Properly matched K will make the structure function as a very effective Priority Queue. The structure size linearly depends on the number and size of elements. PTrie is a clever combination of the idea of prefix tree -- Trie, structure of logarithmic time complexity for insert and remove operations, doubly linked list and queues.