Abstract
In the Multicast k-Tree Routing Problem, a data copy is sent from the source node to at most k destination nodes in every transmission. The goal is to minimize the total cost of sending data to all destination nodes, which is measured as the sum of the costs of all routing trees. This problem was formulated out of optical networking and has applications in general multicasting. Several approximation algorithms, with increasing performance, have been proposed in the last several years; The most recent ones are heavily relied on a tree partitioning technique. In this paper, we present a further improved approximation algorithm along the line. The algorithm has a worst case performance ratio of \(\frac 54\rho + \frac 32\), where ρ denotes the best approximation ratio for the Steiner Minimum Tree problem. The proofs of the technical routing lemmas also provide some insights on why such a performance ratio could be the best possible that one can get using this tree partitioning technique.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Altinkemer, K., Gavish, B.: Heuristics with Constant Error Guarantees for the Design of Tree Networks. Management Science 34, 331–341 (1988)
Bharath-Kumar, K., Jaffe, J.M.: Routing to Multiple Destinations in Computer Networks. IEEE Transaction on Communications 31, 343–351 (1983)
Cai, Z.: Improved Algorithms for Multicast Routing and Binary Fingerprint Vector Clustering. Master’s Thesis, Department of Computing Science, University of Alberta (2004)
Cai, Z., Chen, Z.-Z., Lin, G.-H.: A 3.4713-Approximation Algorithm for the Capacitated Multicast Tree Routing Problem. The Special Issue of Theoretical Computer Science for COCOA 2008 (submitted) (2009)
Cai, Z., Chen, Z.-Z., Lin, G.-H., Wang, L.: An Improved Approximation Algorithm for the Capacitated Multicast Tree Routing Problem. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 286–295. Springer, Heidelberg (2008)
Cai, Z., Lin, G.-H., Xue, G.: Improved Approximation Algorithms for the Capacitated Multicast Routing Problem. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 136–145. Springer, Heidelberg (2005)
Christofides, N.: Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976)
Gröpl, C., Hougardy, S., Nierhoff, T., Prömel, H.J.: Approximation Algorithms for the Steiner Tree Problem in Graphs. In: Du, D.-Z., Cheng, X. (eds.) Steiner Trees in Industries, pp. 235–279. Kluwer Academic Publishers, Dordrecht (2001)
Gu, J., Hu, X.D., Jia, X., Zhang, M.-H.: Routing Algorithm for Multicast under Multi-tree Model in Optical Networks. Theoretical Computer Science 314, 293–301 (2004)
Hu, X.-D., Shuai, T.-P., Jia, X., Zhang, M.-H.: Multicast Routing and Wavelength Assignment in WDM Networks with Limited Drop-offs. In: Proceedings of IEEE INFOCOM (2004)
Huitema, C.: Routing in the Internet. Prentice Hall PTR, Englewood Cliffs (2000)
Jothi, R., Raghavachari, B.: Approximation Algorithms for the Capacitated Minimum Spanning Tree Problem and its Variants in Network Design. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 805–818. Springer, Heidelberg (2004)
Kuo, F., Effelsberg, W., Garcia-Luna-Aceves, J.J.: Multimedia Communications: Protocols and Applications. Prentice Hall, Inc., Englewood Cliffs (1998)
Libeskind-Hadas, R.: Efficient Collective Communication in WDM Networks with a Power Budget. In: Proceedings of the Ninth IEEE Conference on Computer Communications and Networks, pp. 612–616 (2000)
Lin, G.-H.: An Improved Approximation Algorithm for Multicast k-Tree Routing. Journal of Combinatorial Optimization 9, 349–356 (2005)
Morsy, E., Nagamochi, H.: An Improved Approximation Algorithm for Capacitated Multicast Routings in Networks. Theoretical Computer Science 390, 81–91 (2008)
Robins, G., Zelikovsky, A.Z.: Improved Steiner Tree Approximation in Graphs. In: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 770–779 (2000)
Sahasrabuddhe, L.H., Mukherjee, B.: Multicast Routing Algorithms and Protocols: a Tutorial. IEEE Networks 14, 90–102 (2000)
Wang, Z., Crowcroft, J.: Quality-of-Service Routing for Supporting Multimedia Applications. IEEE Journal on Selected Areas in Communications 14, 1228–1234 (1996)
Zhang, X., Wei, J., Qiao, C.: Constrained Multicast Routing in WDM Networks with Sparse Light Splitting. In: Proceedings of IEEE INFOCOM, pp. 1781–1790 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cai, Z., Goebel, R., Lin, G. (2009). Size-Constrained Tree Partitioning: A Story on Approximation Algorithm Design for the Multicast k-Tree Routing Problem. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-02026-1_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02025-4
Online ISBN: 978-3-642-02026-1
eBook Packages: Computer ScienceComputer Science (R0)