Abstract
The edge asymmetry of a directed, edge-weighted graph is defined as the maximum ratio of the weight of antiparallel edges in the graph, and can be used as a measure of the heterogeneity of links in a data communication network. In this paper we provide a near-tight upper bound on the competitive ratio of the Online Steiner Tree problem in graphs of bounded edge asymmetry α. This problem has applications in efficient multicasting over networks with non-symmetric links. We show an improved upper bound of \(O \left (\min \left \{ \max \left \{ \alpha \frac{\log k}{\log \alpha}, \alpha \frac{\log k}{\log \log k} \right \} ,k \right \} \right )\) on the competitive ratio of a simple greedy algorithm, for any request sequence of k terminals. The result almost matches the lower bound of \(\Omega \left (\min \left \{ \max \left \{ \alpha \frac{\log k}{\log \alpha}, \alpha \frac{\log k}{\log \log k} \right \}, k^{1-\epsilon} \right \} \right )\) (where ε is an arbitrarily small constant) due to Faloutsos et al. [8] and Angelopoulos [2].
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References
Angelopoulos, S.: Improved Bounds for the Online Steiner Tree Problem in Graphs of Bounded Edge-Asymmetry. Technical Report CS-2006-36, David R. Cheriton School of Computer Science, University of Waterloo (2006)
Angelopoulos, S.: Improved Bounds for the Online Steiner Tree Problem in Graphs of Bounded Edge-Asymmetry. In: Bansal, N., Pruhs, K., Stein, C. (eds.) Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 248–257. ACM Press, New York (2007)
Awerbuch, B., Azar, Y., Bartal, B.: On-line Generalized Steiner Problem. Theor. Comp. Sci. 324(2–3), 313–324 (2004)
Azar, Y., Alon, N.: On-line Steiner Trees in the Euclidean Plane. Discrete and Computational Geometry 10, 113–121 (1993)
Berman, P., Coulston, C.: Online Algorithms for Steiner Tree Problems. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, pp. 344–353 (1997)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Claffy, K.G., Polyzos, B.H.W.: Traffic Characteristics of the T1 NSFnet Backbone. In: IEEE-Infocom, pp. 885–892 (1993)
Faloutsos, M., Pankaj, R., Sevcik, K.C.: The Effect of Asymmetry on the On-line Multicast Routing Problem. Int. J. Found. Comput. Sci. 13(6), 889–910 (2002)
Imase, M., Waxman, B.: The Dynamic Steiner Tree Problem. SIAM Journal on Discrte Mathematics 4(3), 369–384 (1991)
Oliveira, C.A.S., Pardalos, P.M.: A Survey of Combinatorial Optimization Problems in Multicast Routing. Comput. Oper. Res. 32(8), 1953–1981 (2005)
Ramanathan, S.: Multicast Tree Generation in Networks with Asymmetric Links. IEEE/ACM Trans. Netw. 4(4), 558–568 (1996)
Westbrook, J., Yam, D.C.K.: Linear Bounds for On-line Steiner Problems. Inf. Proc. Ltrs. 55(2), 59–63 (1995)
Westbrook, J., Yan, D.C.K.: The Performance of Greedy Algorithms for the On-line Steiner Tree and Related Problems. Math. Syst. Theory 28(5), 451–468 (1995)
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Angelopoulos, S. (2008). A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry. 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_7
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DOI: https://doi.org/10.1007/978-3-540-87744-8_7
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