| Issue |
RAIRO-Oper. Res.
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2419 - 2436 | |
| DOI | https://doi.org/10.1051/ro/2025082 | |
| Published online | 05 September 2025 | |
Exploring monotone priority queues for Dijkstra optimization
PPGI – Instituto de Computaç˜ao, Universidade Federal do Amazonas, Manaus-AM, Brazil
* Corresponding author: jonas.costa@icomp.ufam.edu.br
Received:
25
November
2024
Accepted:
17
June
2025
The Shortest Path Problem (SPP) is one of the most significant problems in combinatorial optimization. Beyond the vast number of direct applications, the SPP frequently serves as a subroutine in solving other optimization problems. This paper presents a comprehensive review of monotone priority queues, a class of data structures that play a crucial role in solving the SPP efficiently. 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.
Mathematics Subject Classification: 68-02 / 68P05 / 68Q25
Key words: Algorithms / data structures / graph algorithms / priority queues / shortest path problem
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.