Philip N. Klein, "A linear-time approximation scheme for TSP for planar weighted graphs", Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (2005), pp. 647-656, and
Philip N. Klein, "A linear-time approximation scheme for TSP in undirected planar graphs with edge-weights," SIAM Journal on Computing 37 (2008), pp.1926-1952.
Amariah Becker, Eli
Fox-Epstein, Philip N. Klein, and David Meierfrankenfeld,
"Engineering an approximation scheme for traveling salesman in
planar graphs", Proceedings of the Symposium on Experimental
Algorithms, 2017, to appear.
Data files used for experiments on the implementation are available here.