Exploring Monotone Priority Queues for Dijkstra Optimization

TL;DR

This paper reviews the development and application of monotone priority queues in Dijkstra's algorithm, highlighting their structures, complexities, and practical considerations for shortest path computations.

Contribution

It provides a comprehensive overview of monotone priority queues, including their evolution, data structures, and theoretical and practical aspects for shortest path algorithms.

Findings

Analysis of various monotone priority queue data structures

Discussion on theoretical complexities and practical considerations

Historical timeline of development and refinement

Abstract

This paper presents a comprehensive overview of monotone priority queues, focusing on their evolution and application in shortest path algorithms. Monotone priority queues are characterized by the property that their minimum key does not decrease over time, making them particularly effective for label-setting algorithms like Dijkstra's. Some key data structures within this category are explored, emphasizing those derived directly from Dial's algorithm, including variations of multi-level bucket structures and radix heaps. Theoretical complexities and practical considerations of these structures are discussed, with insights into their development and refinement provided through a historical timeline.