Let $H$ be a fixed graph and let $G$ be an $H$-minor free $n$-vertex graph with integer edge weights and no negative weight cycles reachable from a given vertex $s$. We present an algorithm that computes a shortest path tree in $G$ rooted at $s$ in $\tilde{ O}(n^{ 4/3}\log L)$ time, where $L$ is the absolute value of the smallest edge weight. The previous best bound was $\tilde{ O}(n^{ \sqrt{ 11.5}-2}\log L) = O(n^{ 1.392}\log L)$. Our running time matches an earlier bound for planar graphs by Henzinger et al.
Categories: cs.DM