Improved Strongly Polynomial Work-Span Tradeoffs for Directed Single Source Shortest Paths

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

Improved Strongly Polynomial Work-Span Tradeoffs for Directed Single Source Shortest Paths

Data Structures and Algorithms 2026-07-21 v1

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

Abstract

We revisit the single-source shortest paths (SSSP) problem on directed graphs with nonnegative real weights and give a deterministic parallel algorithm with $O(n^{1+o(1)}t^2 + m^{1+o(1)})$ work and $\tilde{O}(n/t)$ span, for any $t \in [1, n]$ . This matches (up to subpolynomial factors) the tradeoff due to [Shi and Spencer '99] for undirected graphs with nonnegative real weights.

Cite

@article{arxiv.2607.19342,
  title  = {Improved Strongly Polynomial Work-Span Tradeoffs for Directed Single Source Shortest Paths},
  author = {Isaac M. Hair and George Z. Li and Jason Li and Junkai Zhang},
  journal= {arXiv preprint arXiv:2607.19342},
  year   = {2026}
}