The traveling salesman problem with few inner points

We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn)O(k!kn) time and O(k)O(k) space, and the second runs in O(2kk2n)O(2kk2n) time and O(2kkn)O(2kkn) space, where nn denotes the number of input points and kk denotes the number of points interior to the convex hull.