Constant factor approximations for the hotlink assignment problem

Abstract

An approach for reducing the navigation effort for the users of a web site is to enhance its hyperlink structure with additional hotlinks. We address the task of adding at most one such additional outgoing edge to each page of a tree-like site, minimizing the path length, i.e. the expected number of "clicks" necessary for the user to reach his destination page. Another common formulation of that problem is to maximize the gain, i.e. the path length reduction achieved by the assignment. In this work we analyze the natural greedy strategy, proving that it reaches the optimal gain up to the constant factor of 2. Considering the gain, we also prove the existence of a PTAS. Finally, we give a polynomial time 2-approximation which constitutes the first constant factor approximation in terms of the path length. The algorithms' performance analyses are made possible by a set of three new basic operations for the transformation of hotlink assignments. © Springer-Verlag Berlin Heidelberg 2007.