On the tollbooth problem
We show that the gap in profit between a naturally defined upward instance of the tollbooth problem on a tree and the original instance can be at least Ω(log log n) where n is the number of edges in the tree.
Sorry, we are unable to provide the full text but you may find it at the following location(s):
http://citeseerx.ist.psu.edu/v... (external link)
http://crab.rutgers.edu/~guyk/... (external link)