The x-and-y-axes travelling salesman problem

The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show that this problem can be solved in polynomial time. The running time of the resulting algorithm is quadratic in the number of cities.

► A special solvable case of the travelling salesman problem (TSP) is considered.
► All cities in this TSP are situated on the x-and-y-axes of the Euclidean plane.
► The problem remained open since 1980.
► The running time of our algorithm is quadratic in the number of cities.