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

We present an implementation and a brief 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 in the comparison-addition model, with running time $O(m \log^{2/3} n)$. We provide a faithful C++ implementation of this algorithm, following all structural details described in the original paper, and compare its empirical performance with the classical Dijkstra's algorithm using binary heaps. The experiments were conducted on both synthetic sparse random graphs and real-world road network instances from the DIMACS benchmark. Our implementation achieves the proposed running time in the worst case. However, our results show that, despite the new algorithm's superior asymptotic complexity, its large constant factors significantly affect its practical performance, making Dijkstra's algorithm faster for all tested sparse graph sizes, including instances with tens of millions of vertices. (This is a work in progress.)