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

2025-11-04

AI Summary

Despite its theoretical asymptotic optimality, the single-source shortest paths (SSSP) algorithm by Duan et al. (2025)—with time complexity $O(m log^{2/3} n)$—lacks a complete, publicly available implementation and empirical evaluation. Method: We present the first faithful C++ implementation of the algorithm, strictly adhering to its core structure and employing hash tables to achieve expected $O(m log^{2/3} n)$ runtime; we benchmark it against binary-heap-optimized Dijkstra’s algorithm on sparse random graphs and real-world road networks. Contribution/Results: Our evaluation reveals that, although theoretically superior, the algorithm incurs substantial constant-factor overhead, rendering it significantly slower than Dijkstra’s on sparse graphs with up to ten million vertices. This work delivers the first reproducible, high-performance implementation and empirically exposes a critical gap between asymptotic optimality and practical efficiency—establishing an essential baseline for future engineering optimizations.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

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 results show that, despite its superior asymptotic complexity, the new algorithm presents significantly larger constant factors, making Dijkstra's algorithm faster for all tested sparse graph sizes, including instances with tens of millions of vertices. Our implementation achieves $O(m log^{2/3} n)$ expected time, due to the use of hash tables, and some possibilities for making it worst-case are being considered. (This is a ongoing work.)

Problem

• Implementing Duan et al.'s algorithm for shortest paths
• Comparing its performance with Dijkstra's algorithm empirically
• Analyzing constant factors despite superior asymptotic complexity

Innovation

• Implements Duan et al. deterministic SSSP algorithm
• Uses hash tables for O(m log^{2/3} n) time
• Compares performance with Dijkstra's binary heap method