#### Theory Seminar

# Energy Efficient Multicommodity Routing

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We consider virtual circuit routing protocols, with an objective of minimizing energy, in a

network of components that are speed scalable, and that may be shutdown when idle. We assume

that the speed s of the router is proportional to its load, and assume the standard model for

component power, namely that the power is some constant static power plus s^b, where typically

bis between 1.1 and 3. We give a polynomial-time off-line algorithm that is the combination of three natural

combinatorial algorithms, and show that for any fixed b the algorithm has approximation ratio

O(log^b k), where k is the number of demand pairs. The algorithm extends rather naturally to

a randomized online algorithm, which we show has competitive ratio O~(log^{3b+1} k). This is the

first online result for the problem. We also show that this online algorithm has competitive

ratio O~(log^{b+1} k) for the case that all connections have a common source.

Joint work with Antonios Antoniadis, Sungjin Im, Ravishankar Krishnaswamy, Benjamin Moseley, Kirk Pruhs, and Cliff Stein: