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 {ai,bi: i=1,…, n} such
that for any 1≤i, j≤n,i≠j,C′(i,j)=C(i,j)+ai+bj [7]. One of the 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.
A SOLVABLE CASE OF THE TRAVELING SALESMAN PROBLEM
