THE EUCLIDEAN TRAVELING SALESMAN PROBLEM AND A SPACE-FILLING CURVE

We elucidate the relationship between space-filling curves and the Euc lidean Traveling(2) Salesman Problem (TSP) by reference to a particula r space-filling curve whose scaling behaviour is strongly related to t he conjectured scaling behaviour of the optimal TSP tour. We suggest t hat space-filling curves can be used to generate testbed TSPs: sets of points which in the limit cover a planar surface and for which tours of minimum length are known.