Comment:
Generalization to d dimensions for d constant also admits a
PTAS [32].
In Rm the problem is APX-complete for any lp metric [429].
The variation in which an integer
is given in the input and
only at least k of the cities must be included in the tour
also admits a PTAS [31].
Minimum geometric angular TSP,
the variation in which the sum of the direction changes in the tour is
minimized, is approximable within
.
The same bound is valid also when there may be several tours covering all the
cities [4].
The maximum geometric traveling salesperson problem (finding the tour of
maximum length) admits a PTAS [61].
Variation in which the input is given as k possibly overlapping
simple polygons in the plane, and where the objective is to find the
shortest tour that visits (intersects) each polygon, is approximable
within
[354].