Bounds for the traveling salesman paths of two-dimensional modular   lattices
  We present tight upper and lower bounds for the traveling salesman path through the points of two-dimensional modular lattices. We use these results to bound the traveling salesman path of two-dimensional Kronecker point sets. Our results rely on earlier work on shortest vectors in lattices as well as on the strong convergence of Jacobi-Perron type algorithms. 
Florian Pausinger
math.CO math.NT