Optimizing Dijkstra for real-world performance

TL;DR

This paper presents a new, faster queue design for Dijkstra's algorithm, significantly improving performance on large graphs and outperforming existing implementations like Boost.

Contribution

Introduces an optimized queue structure for Dijkstra's algorithm that enhances real-world performance and is easy to implement.

Findings

Prototype runs twice as fast as Boost on large graphs

Implementation achieved in a few weeks by a single programmer

Design shows promise for practical, high-performance shortest path computations

Abstract

Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap as its internal queue, it has been noted that in practice, a binary (or $d$-ary) heap implementation is significantly faster. This paper introduces an even faster queue design for the algorithm. Our experimental results currently put our prototype implementation at about twice as fast as the Boost implementation of the algorithm on both real-world and generated large graphs. Furthermore, this preliminary implementation was written in only a few weeks, by a single programmer. The fact that such an early prototype compares favorably against Boost, a well-known open source library developed by expert programmers, gives us reason to believe our design for the queue is indeed better suited to the problem at hand, and the favorable time measurements are not a product of any specific implementation technique we employed.