The Euclidean TSP problem on a set P of points in the plane is to compute a shortest tour visiting all the points in P, that is, a tour whose (Euclidean) length is minimized. Suppose we have an algo- rithm Integer TSP(P) that, given a set P of n points in the plane with integer coordinates in the range 0, 1,..., m, computes a shortest tour in O(nm) time. However, in general, coordinates need not be integral and we do not have a pre-specified range in which the coordinates lie. We will assume though that min p = min P, = 0, PEP PEP where pe and p, denote the r- and y-coordinate of the point p. Consider the following PTAS for the general Euclidean TSP problem which simply rounds the coordinates to integers and then applies the IntegerTSP al- gorithm. PTAS-TSP(P, e) 1. A +... = 2. For each point p EP define p = (pe Py) where p = [P/A] and py [Py/A]. Let P ={p' \ p = P}. 3. Compute a shortest tour on P' using the algorithm Integer TSP, and return the reported tour (with each point p/ replaced with its corresponding point PEP. Find a suitable value of A and prove that for your choice of A: length(T) (1+e)OPT, where T is the tour returned by the algorithm, length(T) is its length, and OPT is the length of an optimal tour on P. Also show that the running time of the algorithm remains polynomial for your choice of A. (Assuming e is constant.)