Bellman-Ford in Almost-Linear Time

Isaac M. Hair; George Z. Li; Jason Li; Junkai Zhang

Bellman-Ford in Almost-Linear Time

Data Structures and Algorithms 2026-07-21 v1

Authors: Isaac M. Hair , George Z. Li , Jason Li , Junkai Zhang

Abstract

We consider the single-source shortest paths problem on a directed graph with real-valued (possibly negative) edge weights and solve this problem in $m^{1+o(1)}$ time.

Cite

@article{arxiv.2607.19346,
  title  = {Bellman-Ford in Almost-Linear Time},
  author = {Isaac M. Hair and George Z. Li and Jason Li and Junkai Zhang},
  journal= {arXiv preprint arXiv:2607.19346},
  year   = {2026}
}