Abstract
In this work, we study the advice complexity of the online minimum Steiner tree problem (ST). Given a (known) graph G = (V,E) endowed with a weight function on the edges, a set of N terminals are revealed in a step-wise manner. The algorithm maintains a sub-graph of chosen edges, and at each stage, chooses more edges from G to its solution such that the terminals revealed so far are connected in it. In the standard online setting this problem was studied and a tight bound of O(log(N)) on its competitive ratio is known. Here, we study the power of non-uniform advice and fully characterize it. As a first result we show that using q ·log(|V|) advice bits, where 0 ≤ q ≤ N − 1, it is possible to obtain an algorithm with a competitive ratio of O(log(N/q). We then show a matching lower bound for all values of q, and thus settle the question.
This work was partially supported by SNF grant 200021141089.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)
Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press (1998)
Böckenhauer, H.-J., Komm, D., Královič, R., Rossmanith, P.: On the advice complexity of the knapsack problem. In: Fernández-Baca, D. (ed.) LATIN 2012. LNCS, vol. 7256, pp. 61–72. Springer, Heidelberg (2012)
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)
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)
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)
Imase, M., Waxman, B.M.: Dynamic steiner tree problem. SIAM J. Discrete Math. 4(3), 369–384 (1991)
Alon, N., Azar, Y.: On-line steiner trees in the euclidean plane. In: Symposium on Computational Geometry, pp. 337–343 (1992)
Berman, P., Coulston, C.: On-line algorithms for steiner tree problems (extended abstract). In: Leighton, F.T., Shor, P.W. (eds.) STOC, pp. 344–353. ACM (1997)
Awerbuch, B., Azar, Y., Bartal, Y.: On-line generalized steiner problem. Theor. Comput. Sci. 324(2-3), 313–324 (2004)
Garg, N., Gupta, A., Leonardi, S., Sankowski, P.: Stochastic analyses for online combinatorial optimization problems. In: Teng, S.H. (ed.) SODA, pp. 942–951. SIAM (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Barhum, K. (2014). Tight Bounds for the Advice Complexity of the Online Minimum Steiner Tree Problem. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-04298-5_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04297-8
Online ISBN: 978-3-319-04298-5
eBook Packages: Computer ScienceComputer Science (R0)