  The power consumption of enormous network devices in data centers has emerged
as a big concern to data center operators. Despite many
traffic-engineering-based solutions, very little attention has been paid on
performance-guaranteed energy saving schemes. In this paper, we propose a novel
energy-saving model for data center networks by scheduling and routing
"deadline-constrained flows" where the transmission of every flow has to be
accomplished before a rigorous deadline, being the most critical requirement in
production data center networks. Based on speed scaling and power-down energy
saving strategies for network devices, we aim to explore the most energy
efficient way of scheduling and routing flows on the network, as well as
determining the transmission speed for every flow. We consider two general
versions of the problem. For the version of only flow scheduling where routes
of flows are pre-given, we show that it can be solved polynomially and we
develop an optimal combinatorial algorithm for it. For the version of joint
flow scheduling and routing, we prove that it is strongly NP-hard and cannot
have a Fully Polynomial-Time Approximation Scheme (FPTAS) unless P=NP. Based on
a relaxation and randomized rounding technique, we provide an efficient
approximation algorithm which can guarantee a provable performance ratio with
respect to a polynomial of the total number of flows.
