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

RESUMO

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 $\log n$.