Has anyone read the new paper from April 2025 that claims a faster algorithm for the directed, non-negative weights single-source shortest path problem?
They claim a deterministic time complexity of $$$O(m \log^{2/3} n)$$$, which would beat the long-assumed $$$\Omega(n \log n)$$$ lower bound on sparse graphs.
Link: https://arxiv.org/abs/2504.17033
Is this legit, and has anyone attempted to implement this yet?
I am looking for a reference implementation in any language (preferably in C++, Java, Rust, or Python).
I would be interested in any links, repositories, or performance comparisons that are available, as I was unable to find any online.
I am also curious about any thoughts on this paper from the Codeforces community.
Thanks!
:)
UPD: I think the paper is legit since it was accepted into STOC 2025 and won the best paper award.
It was accepted here and won the best paper award in the schedule here.









