Multicast routing for energy minimization using speed scaling

Authors:
Nikhil Bansal;Anupam Gupta;Ravishankar Krishnaswamy;Viswanath Nagarajan;Kirk Pruhs;Cliff Stein
Affiliations:
Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;Computer Science, Carnegie Mellon University, United States;Computer Science, Princeton University, United States;IBM T.J. Watson Research Center, United States;Computer Science, University of Pittsburgh, United States;Industrial Engineering and Operations Research, Columbia University, United States
Venue:
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Year:
2012

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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+fα, where σ is the static power, and α1 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 ti a routing path (the virtual circuit) Pi connecting a fixed source s to sink ti 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.