A generalization of the convex-hull-and-line traveling salesman problem

Two instances of the traveling salesman problem, on the same node set (1,2 n} but with different cost matrices C and C , are equivalent iff there exist {a, hi:-1, n} such that for any 1 _ i, j _ n, j, C(i, j) C(i,j) q-at -bj [7]. One ofthe well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP.