We propose a novel architecture of data center networks (DCN), which adds wireless network card to both servers and routers. Existing traffic redundancy elimination (TRE) mechanisms reduce link loads and increase network capacity in several environments by removing strings that have appeared in earlier packets through encoding and decoding them several hops downstream. This article is the first to explore TRE mechanisms in large-scale DCNs and the first to exploit cooperative TRE among servers. Moreover, it also achieves the `logically centralized' control over the physically distributed states in emerging software defined networks (SDN) paradigm, by sharing information among servers and routers in data centers with wireless cards. We first formulate the TREDaCeN (TRE in Data Center Networks) problem and reduce the cycle cover problem to prove that finding an optimal caching task assignment for TREDaCeN problem is NP-hard. We further describe an offline TREDaCeN algorithm which is proved to have good approximation ratio. We then discuss efficient online zero-delay and semi-distributed implementations of TREDaCeN supported by physical proximity of servers and routers, enabling status updates in a single wireless transmission, using an efficient prioritized schedule. We also address online cache replacement and consistency of information in servers and routers with and without delay. Our framework is tested on different parameters and shows superior performance in comparison to other mechanisms (imported directly to this setting). Our results show the robustness and the trade-off between the `logically centralized' implementation and the overhead on handling inconsistency of distributed information in DCN.