Abstract
We consider virtual circuit multicast routing in a network of links that are speed scalable. We assume that a link with load f uses power σ + f α, where σ is the static power, and α > 1 is some constant. We assume that a link may be shutdown if not in use. In response to the arrival of client i at vertex t i a routing path (the virtual circuit) P i connecting a fixed source s to sink t i must be established. The objective is to minimize the aggregate power used by all links.
We give a polylog-competitive online algorithm, and a polynomial-time O(α)-approximation offline algorithm if the power functions of all links are the same. If each link can have a different power function, we show that the problem is APX-hard. If additionally, the edges may be directed, then we show that no poly-log approximation is possible in polynomial time under standard complexity assumptions. These are the first results on multicast routing in speed scalable networks in the algorithmic literature.
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
Proceedings of the vision and roadmap workshop on routing telecom and data centers toward efficient energy use (October 2008)
Andrews, M., Antonakopoulos, S., Zhang, L.: Minimum-cost network design with (dis)economies of scale. In: FOCS, pp. 585–592 (2010)
Andrews, M., Fernández, A., Zhang, L., Zhao, W.: Routing for energy minimization in the speed scaling model. In: INFOCOM, pp. 2435–2443 (2010)
Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line routing of virtual circuits with applications to load balancing and machine scheduling. J. ACM 44(3), 486–504 (1997)
Benoit, A., Melhem, R., Renaud-Goud, P., Robert, Y.: Power-aware manhattan routing on chip multiprocessors. In: IEEE International Parallel and Distributed Processing Symposium (IPDPS) (May 2012)
Chakrabarty, D., Chekuri, C., Khanna, S., Korula, N.: Approximability of Capacitated Network Design. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 78–91. Springer, Heidelberg (2011)
Gafni, E.M., Bertsekas, D.P.: Path assignment for virtual circuit routing. In: Proceedings of the Symposium on Communications Architectures & Protocols, SIGCOMM 1983, pp. 21–25. ACM, New York (1983)
Gupta, A., Krishnaswamy, R., Pruhs, K.: Online primal-dual for non-linear optimization with applications to speed scaling. CoRR, abs/1109.5931 (2011)
Imase, M., Waxman, B.M.: Dynamic Steiner tree problem. SIAM J. Discrete Math. 4(3), 369–384 (1991)
Johnson, W.B., Schechtman, G., Zinn, J.: Best constants in moment inequalities for linear combinations of independent and exchangeable random variables. Ann. Probab. (1), 234–253 (1985)
Kim, J., Horowitz, M.A.: Adaptive supply serial links with sub-1-v operation and per-pin clock recovery. IEEE Journal of Solid-State Circuits 37(11), 1403–1413 (2002)
Raz, R.: A parallel repetition theorem. SIAM J. Comput. 27(3), 763–803 (1998)
Rosenthal, H.P.: On the subspaces of L p (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8, 273–303 (1970)
Trevisan, L.: Non-approximability results for optimization problems on bounded degree instances. In: ACM Symposium on Theory of Computing, pp. 453–461 (2001)
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
Bansal, N., Gupta, A., Krishnaswamy, R., Nagarajan, V., Pruhs, K., Stein, C. (2012). Multicast Routing for Energy Minimization Using Speed Scaling. In: Even, G., Rawitz, D. (eds) Design and Analysis of Algorithms. MedAlg 2012. Lecture Notes in Computer Science, vol 7659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34862-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-34862-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34861-7
Online ISBN: 978-3-642-34862-4
eBook Packages: Computer ScienceComputer Science (R0)