We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth ω is n^(O(log²ω) when the edge arrival functions are piecewise linear. This is an improvement on the bound of n^(Θ(log n))by Foschini, Hershberger, and Suri for graphs without any bound on treewidth. We provide an algorithm for calculating this arrival function using star-mesh transformations, a generalization of the wye-delta-wye transformations.
Key Words: treewidth, time-dependent shortest paths, star-mesh transformation
