Optimal approximability of bookmark assignments

Consider a rooted directed acyclic graph G=(V,E) with root r, representing a collection V of web pages connected via a set E of hyperlinks. Each node v is associated with the probability that a user wants to access the node v. The access cost is defined as the expected number of steps required to reach a node from the root r. A bookmark is an additional shortcut from r to a node of G, which may reduce the access cost. The bookmark assignment problem is to find a set of bookmarks that achieves the greatest improvement in the access cost. For the problem, the paper shows the tight bound on the (in)approximability under the assumption P≠NP: we present a polynomial time approximation algorithm with factor (1-1/e), and show that there exists no polynomial time approximation algorithm with a better constant factor than (1-1/e) unless P=NP.