A Faster Directed Single-Source Shortest Path Algorithm

2026-02-08

AI Summary

This work addresses the single-source shortest paths (SSSP) problem with non-negative edge weights in directed graphs, focusing on efficient deterministic algorithms for sparse graphs. The authors propose a novel algorithm that integrates a refined path relaxation strategy with an efficient data structure, achieving a time complexity of $O(m \sqrt{\log n} + \sqrt{mn \log n \log \log n})$. This bound improves upon the previous best-known deterministic result of $O(m \log^{2/3} n)$ for sparse instances. By maintaining determinism while significantly enhancing computational efficiency, the proposed method attains the current best theoretical running time for SSSP in sparse directed graphs with non-negative weights.

Technology Category

• Planning, Routing, and Scheduling: Deterministic Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log \log n})$ for sparse graphs. This improves the recent breakthrough result of $O(m\log^{2/3} n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].

Problem

• single-source shortest paths
• directed graphs
• non-negative edge weights
• deterministic algorithm
• running time

Innovation

• single-source shortest paths
• directed graphs
• deterministic algorithm
• time complexity
• graph algorithms