Tree Traveling Salesman Problems

	The well known Gilmore-Gomory Traveling Salesman Problem can be thought of as the 
following problem: Given line segments of a line, and the direction of traversal of each 
segment, we need to know the order in which these should be traversed so as to minimize the 
total distance traversed; note that the distance traversed from the end of one segement to
the beginning of the next is wasted and it is this waste that we want to minimize. The 
generalization considered here is two fold: first we can choose the direction of traversal
of each segment and second the these are line segments corresponding to paths in a tree
between specified nodes. We show tha this problem is in general NP-hard.