Implementation and Brief Experimental Analysis of the Duan et al. (2025) Algorithm for Single-Source Shortest Paths

TL;DR

This paper implements and tests Duan et al.'s 2025 algorithm for the Single-Source Shortest Path problem, revealing that large constant factors limit its practical advantage over Dijkstra's algorithm despite favorable asymptotic bounds.

Contribution

It provides the first practical C++ implementation of Duan et al.'s algorithm and compares its performance with Dijkstra's algorithm on large graphs.

Findings

The algorithm matches theoretical complexity but has large constant factors.

Dijkstra's algorithm is 3-4 times faster in tested scenarios.

The new algorithm would need an astronomically large number of vertices to outperform Dijkstra's.

Abstract

We present an implementation and experimental analysis of the deterministic algorithm proposed by Duan et al. (2025) for the Single-Source Shortest Path (SSSP) problem, which achieves the best-known asymptotic upper bound of $O(m \log^{2/3} n)$. We provide a worst-case C++ implementation of this algorithm utilizing $O(n \log^{1/3} n)$ space, as well as a variant that reduces memory usage to $O(n)$ while maintaining the same time complexity in expectation. We compare these implementations against Dijkstra's algorithm on sparse random graphs, grids, and U.S. road networks with up to 10 million vertices. Our results show that while the implementations adhere to their theoretical complexity bounds, large constant factors hinder their practical utility; Dijkstra's algorithm remains 3 to 4 times faster in all tested scenarios. Furthermore, we estimate that the number of vertices would need to vastly exceed $10^{67}$ for the worst-case implementation to outperform Dijkstra's. These findings suggest that a substantial reduction in constant factors is required before this theoretical breakthrough can displace established methods in practical applications.