6.1.2 Divide Anhd Conquer

First, we will assume without loss of generality that the points are contained within a minimum bounding box with side length n2. Second, we will assume all points have integer coordinates. It can be shown that this modification can add no more than 2 √ 2n to the total length of an optimal tour in the transformed instance (see previous lecture). Also, note that this rounding may ’collapse’ several nearby points to the same coodrdinates. This means that the distance between any two points in our tranformed instance must be either 0 or ≥ 1.