Abstract
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 presents a polynomial time approximation algorithm with factor (1 − 1/e), and shows that there exists no polynomial time approximation algorithm with a better constant factor than (1 − 1/e) unless \({\cal NP}\subseteq {\cal DTIME}(N^{O(\log\log N)})\), where N is the size of the inputs.
This work is partially supported by Grant-in-Aid for Scientific Research on Priority Areas No. 16092222 and 16092223, and by Grant-in-Aid for Young Scientists (B) No. 17700022, No. 18700014 and No. 18700015.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alpern, B., Hoover, R., Rosen, B.K., Sweeney, P.F., Zadeck, F.K.: Incremental evaluation of computational circuits. In: Proc. SODA 1990, pp. 32–42 (1990)
Arora, S., Lund, C.: Hardness of Approximation. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-hard problems, pp. 399–446. PWS publishing company (1995)
Bose, P., Kranakis, E., Krizanc, D., Vergas Martin, M., Czyzowicz, J., Pelc, A., Gasieniec, J.: Strategies for hotlink assignments. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 23–34. Springer, Heidelberg (2000)
Czyzowicz, J., Kranakis, E., Krizanc, D., Pelc, A., Vergas Martin, M.: Assigning bookmarks in perfect binary trees. Ars Combinatoria, vol. LXXXII (2007)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Fuhrmann, S., Krumke, S.O., Wirth, H.-C.: Multiple hotlink assignment. In: Brandstädt, A., Le, V.B. (eds.) WG 2001. LNCS, vol. 2204, pp. 189–200. Springer, Heidelberg (2001)
Feige, U., Langberg, M.: Approximation algorithms for maximization problems arising in graph partitioning. J. Algorithms 41(2), 174–211 (2001)
Khuller, S., Moss, A., Naor, J.: The budgeted maximum coverage problem. IPL 70(1), 39–45 (1999)
Langberg, M.: Approximation Algorithms for Maximization Problems arising in Graph Partitioning. M. Sc. thesis, Weizmann Institute of Science (1998)
Li, B., Deng, X., Golin, M.J., Sohraby, K.: On the optimal placement of web proxies in the Internet: Linear Topology. In: Proc. HPN 1998, pp. 485–495 (1998)
Li, B., Golin, M.J., Italiano, G.F., Deng, X., Sohraby, K.: On the optimal placement of web proxies in the Internet. In: Proc. INFOCOMM 1999, pp. 1282–1290 (1999)
Marchetti-Spaccamela, A., Nanni, U., Rohnert, H.: Maintaining a topological order under edge insertions. IPL 59(1), 53–58 (1996)
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)
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)
Nemhauser, G., Wolsey, L., Fisher, M.: An analysis of the approximations for maximizing submodular set functions. Mathematical Programming 14, 265–294 (1978)
Petrank, E.: The hardness of approximation: gap location. Computational Complexity 4, 133–157 (1994)
Perkowitz, M., Etzioni, O.: Towards adaptive web sites: conceptual framework and case study. Computer Networks 31, 1245–1258 (1999)
Pessoa, A.A., Laber, E.S., 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)
Vergas Martin, M.: Enhancing Hyperlink Structure for Improving Web Performance. PhD thesis, School of Computer Science, Carleton University (2002)
Vohra, R.V., Hall, N.G.: A probabilistic analysis of the maximal covering location problem. Discrete Applied Mathmatics 43(2), 175–183 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Asahiro, Y., Miyano, E., Murata, T., Ono, H. (2007). On Approximation of Bookmark Assignments . In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-74456-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74455-9
Online ISBN: 978-3-540-74456-6
eBook Packages: Computer ScienceComputer Science (R0)