A linear-time approximation scheme for planar weighted TSP
Philip N. Klein · 2005
In view of the fact that an /spl epsi/-optimal tour can be found in the Euclidean case in time that it is polynomial with a fixed degree, independent of /spl epsi/, it seems natural to ask whether the same holds true for the planar case. We give an algorithm requiring O(c/sup 1/c2/ n) time to find an /spl epsi/-optimal traveling salesman tour in the metric defined by a planar graph with nonnegative edge-lengths.