On the complexity of optimal hotlink assignment

Abstract

The concept of hotlink assignment aims at reducing the navigation effort for users of a web directory or similar structure by inserting a limited number of additional hyperlinks called hotlinks. Given an access probability distribution of the leaves of the tree representing the web site, the goal of hotlink assignment algorithms is to minimize the expected path length between the root and the leaves. We prove that this optimization problem is NP-hard, even if only one outgoing hotlink is allowed for each node. This answers a question that has been open since the first formulation of the problem in [3]. In this work we also investigate the model where hotlinks are only allowed to point at the leaves of the tree. We demonstrate that for this model optimal solutions can be computed in polynomial time. Our algorithm operates in a very general setting, where the maximum number of outgoing hotlinks is specified individually for each node. Experimental evaluation shows that the algorithm is applicable in practice. © 2008 Springer-Verlag Berlin Heidelberg.