A Faster Directed Single-Source Shortest Path Algorithm

TL;DR

This paper introduces a faster deterministic algorithm for directed single-source shortest paths on non-negative weighted graphs, improving upon recent state-of-the-art algorithms with better theoretical running time.

Contribution

It proposes a novel deterministic algorithm with improved asymptotic running time for directed SSSP, especially in sparse graphs, advancing the theoretical understanding of shortest path computations.

Findings

Achieves $O(mrac{ ext{sqrt(log n)}}{}+ ext{sqrt}(mn ext{log n} ext{log log n}))$ time complexity

Improves the recent $O(m ext{log}^{2/3} n)$ time bound for directed SSSP

Provides a deterministic approach with better performance bounds for real non-negative edge-weighted directed graphs.

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].