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The power consumption of enormous network devices in data centers has emergedas a big concern to data center operators. Despite manytraffic-engineering-based solutions, very little attention has been paid onperformance-guaranteed energy saving schemes. In this paper, we propose a novelenergy-saving model for data center networks by scheduling and routing"deadline-constrained flows" where the transmission of every flow has to beaccomplished before a rigorous deadline, being the most critical requirement inproduction data center networks. Based on speed scaling and power-down energysaving strategies for network devices, we aim to explore the most energyefficient way of scheduling and routing flows on the network, as well asdetermining the transmission speed for every flow. We consider two generalversions of the problem. For the version of only flow scheduling where routesof flows are pre-given, we show that it can be solved polynomially and wedevelop an optimal combinatorial algorithm for it. For the version of jointflow scheduling and routing, we prove that it is strongly NP-hard and cannothave a Fully Polynomial-Time Approximation Scheme (FPTAS) unless P=NP. Based ona relaxation and randomized rounding technique, we provide an efficientapproximation algorithm which can guarantee a provable performance ratio withrespect to a polynomial of the total number of flows.

Energy-Efficient Flow Scheduling and Routing with Hard Deadlines in Data Center Networks