Abstract
We consider the model of online computation with advice [5]. In particular, we study the k-server problem under this model. We prove two upper bounds for this problem. First, we show a \(\Big\lceil\frac{\lceil\log k\rceil}{b-2}\Big\rceil \)-competitive online algorithm for general metric spaces with b bits of advice per request, where 3 ≤ b ≤ logk. This improves upon the recent result of [1]. Moreover, we believe that our algorithm and our analysis are more intuitive and simpler than those of [1]. Second, we give a 1-competitive online algorithm for trees which uses 2 + 2⌈log(p + 1)⌉ bits of advice per request, where p is the caterpillar dimension of the tree.
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
Böckenhauer, H.-J., Komm, D., Královic, R., Královic, R.: On the Advice Complexity of the k-Server Problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 207–218. Springer, Heidelberg (2011) see also technical report at, ftp://ftp.inf.ethz.ch/pub/publications/tech-reports/7xx/703.pdf
Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: On the Advice Complexity of Online Problems. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 331–340. Springer, Heidelberg (2009)
Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press, New York (1998)
Dobrev, S., Královič, R., Pardubská, D.: How Much Information About the Future is Needed? In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 247–258. Springer, Heidelberg (2008)
Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. Theor. Comput. Sci. 412(24), 2642–2656 (2011)
Hromkovič, J., Královič, R., Královič, R.: Information Complexity of Online Problems. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 24–36. Springer, Heidelberg (2010)
Komm, D., Královič, R.: Advice Complexity and Barely Random Algorithms. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 332–343. Springer, Heidelberg (2011)
Matoušek, J.: On embedding trees into uniformly convex banach spaces. Israel Journal of Mathematics 114, 221–237 (1999), http://dx.doi.org/10.1007/BF02785579 , doi:10.1007/BF02785579
Renault, M.: Online Algorithms with Advice. Master’s thesis, MPRI – Université Paris Diderot - Paris 7 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Renault, M.P., Rosén, A. (2012). On Online Algorithms with Advice for the k-Server Problem. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-29116-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29115-9
Online ISBN: 978-3-642-29116-6
eBook Packages: Computer ScienceComputer Science (R0)