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

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