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We study network optimization that considers energy minimization as an objective. Studies have shown that mechanisms such as speed scaling can significantly reduce the power consumption of telecommunication networks by matching the consumption of each network element to the amount of processing required for its carried traffic. Most existing research on speed scaling focuses on a single network element in isolation. We aim for a network-wide optimization. Specifically, we study a routing problem with the objective of provisioning guaranteed speed/bandwidth for a given demand matrix while minimizing energy consumption. Optimizing the routes critically relies on the characteristic of the energy curve $f(s)$, which is how energy is consumed as a function of the processing speed $s$. If $f$ is superadditive, we show that there is no bounded approximation in general for integral routing, i.e., each traffic …