Size-Sensitive Padded Decompositions for Faster Deterministic Negative-Weight Shortest Paths

Abstract

We give a deterministic algorithm for single-source shortest paths in directed graphs with integral edge weights at least $-W$ that runs in time $$O((m+n\log \log n){\log }^{2}n\log (nW)).$$ This improves the previous fastest deterministic bound of Li by a factor of $\log n$.

v2 improves on v1 by log log n