Computing the Fr\'echet distance of trees and graphs of bounded tree width

We give algorithms to compute the Fr'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n\log n})$ time for trees of arbitrary degree. For graphs of bounded tree width we show one can compute the Fr'echet distance in FPT (fixed parameter tractable) time.