A Faster Directed Single-Source Shortest Path Algorithm
Ran Duan, Xiao Mao, Xinkai Shu, Longhui Yin
TL;DR
The paper addresses deterministic SSSP on directed graphs with non-negative weights under the comparison-addition model, achieving a running time of $O(m\\sqrt{\\log n} +\\sqrt{mn\\log n\\log\\log n})$ and improving the previous directed bound of $O(m\\log^{2/3} n)$. It introduces a bounded multi-source shortest path (BMSSP) framework that uses a frontier-based, pivot-driven divide-and-conquer strategy to reduce per-vertex work and avoids full sorting by organizing the frontier into edge-disjoint subtrees. Key innovations include degree-reduction preprocessing, a pivot-based frontier partitioning scheme, and a block-based data structure enabling efficient frontier management with amortized $O(t)$ per operation, where $t$ is tuned to optimize the bound. The approach yields a near-linear-time result for sparse graphs and matches the best known performance for undirected SSSP in a deterministic directed setting, marking a significant advance in deterministic algorithms for directed SSSP with real non-negative weights.
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].