Multicast Routing for Energy Minimization Using Speed Scaling
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.
KeywordsPower Function Steiner Tree Online Algorithm Vertex Cover Satisfying Assignment
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