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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Karpf, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Perkowitz, M., Etzioni, O.: Towards adaptive web sites: Conceptual framework and case study. Computer Networks 31(11-16), 1245–1258 (1999)
Bose, P., Czyzowicz, J., Gasienicz, L., Kranakis, E., Krizanc, D., Pelc, A., Vargas Martin, M.: Strategies for hotlink assignments. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969. Springer, Heidelberg (2000)
Czyzowicz, J., Kranakis, E., Krizanc, D., Pelc, A., Vargas Martin, M.: Evaluation of hotlink assignment heuristics for improving web access. In: Proceedings of the 2nd International Conference on Internet Computing (ICOMP) (2001)
Kranakis, E., Krizanc, D., Shende, S.: Approximate hotlink assignment. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223. Springer, Heidelberg (2001)
Bose, P., Krizanc, D., Langerman, S., Morin, P.: Asymmetric communication protocols via hotlink assignments. In: Proceeding of the 9th Colloquium on Structural Information and Communication Complexity (SIROCCO) (2002)
Czyzowicz, J., Kranakis, E., Krizanc, D., Pelc, A., Vargas Martin, M.: Enhancing hyperlink structure for improving web performance. Journal of Web Engineering 1(2), 93–127 (2003)
Gerstel, O., Kutten, S., Matichin, R., Peleg, D.: Hotlink enhancement algorithms for web directories. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 68–77. Springer, Heidelberg (2003)
Matichin, R., Peleg, D.: Approximation algorithm for hotlink assignments in web directories. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 271–280. Springer, Heidelberg (2003)
Li, K., Shen, H.: Optimal placement of web proxies for tree networks. In: IEEE International Conference on e-Technology, e-Commerce and e-Service (EEE 2004) (2004)
Matichin, R., Peleg, D.: Approximation algorithm for hotlink assignment in the greedy model. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 233–244. Springer, Heidelberg (2004)
Pessoa, A., Laber, E., de Souza, C.: Efficient algorithms for the hotlink assignment problem: The worst case search. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 778–792. Springer, Heidelberg (2004)
Pessoa, A., Laber, E., de Souza, C.: Efficient implementation of a hotlink assignment algorithm for Web sites. In: Proceedings of the 6th Workshop on Algorithm Engineering and Experiments (ALENEX) and the First Workshop on Analytic Algorithmics and Combinatorics (ANALCO) (2004)
Douïeb, K., Langerman, S.: Dynamic hotlinks. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 182–194. Springer, Heidelberg (2005)
Douïeb, K., Langerman, S.: Near-entropy hotlink assignments. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 292–303. Springer, Heidelberg (2006)
Jacobs, T.: Constant factor approximations for the hotlink assignment problem. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 188–200. Springer, Heidelberg (2007)
Jacobs, T.: An experimental study of recent hotlink assignment algorithms. In: Proc. of the Workshop on Algorithm Engineering and Experiments (ALENEX) and the First Workshop on Analytic Algorithmics and Combinatorics (ANALCO) (2008)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jacobs, T. (2008). On the Complexity of Optimal Hotlink Assignment. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-87744-8_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87743-1
Online ISBN: 978-3-540-87744-8
eBook Packages: Computer ScienceComputer Science (R0)