We give an algorithm requiring $O(c^{1/\epsilon^2}n)$ time to find an $\epsilon$-optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edge-lengths. For the case of all lengths equal to 1, the time required is $O(c^{1/\epsilon} n)$.
['Philip N. Klein']
A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights