Exploring monotone priority queues for Dijkstra optimization

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.