Approximation Algorithm for Hotlink Assignment in the Greedy Model

Link-based information structures such as the web can be enhanced through the addition of hotlinks. Assume that each node in the information structure is associated with a weight representing the access frequency of the node by users. In order to access a particular node, the user must follow a path leading to it from the root. By adding new hotlinks to the tree, it may be possible to reduce the access cost of the system, namely, the expected number of steps needed to reach a leaf from the root, assuming the user can decide which hotlinks to follow in each step. The hotlink assignment problem involves finding a set of hotlinks (with at most K = O(1) hotlinks emanating from every node) maximizing the gain in the expected cost. The paper addresses this problem in two user models, namely, the traditional clairvoyant user model employed in [P. Bose, J. Czyzowicz, L. Gasieniec, E. Kranakis, D. Krizanc, A. Pelc, M.V. Martin, Strategies for hotlink assignments, in: Proc. 11th Symp. on Algorithms and Computation, 2000, pp. 23–34; E. Kranakis, D. Krizanc, S. Shende, Approximating hotlink assignments, in: Proc. 12th Symp. on Algorithms and Computation, 2001, pp. 756–767; P. Bose, D. Krizanc, S. Langerman, P. Morin, Asymmetrical communication protocols via hotlink assignments, in: Proc. 9th Colloq. on Structural Information and Communication Complexity, 2002, pp. 33–39; R. Matichin, D. Peleg, Approximation algorithm for hotlink assignments in web directories, in: Proc. Workshop on Algorithms and Data Structures, 2003, pp. 271–280] and the more realistic greedy user model recently introduced in [O. Gerstel, S. Kutten, R. Matichin, D. Peleg, Hotlink enhancement algorithms for web directories, in: Proc. 14th Symp. on Algorithms and Computation, 2003, pp. 68–77], and presents a polynomial time 2-approximation algorithm for the hotlink assignment problem on rooted directed trees. c © 2007 Elsevier B.V. All rights reserved.