Hallucination Helps: Energy Efficient Virtual Circuit Routing

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, where typically α ∈ [1.1, 3]. We give a polynomial-time offline algorithm that is the combination of three natural combinatorial algorithms, and show that for any fixed α the algorithm has approximation ratio O(log 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 Õ(log k). This is the first online result for the problem. We also show that this online algorithm has competitive ratio Õ(log k) for the case that all connections have a common source.