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Resource allocation is one of the most important challenges in operating a data center. We investigate allocation of two main types of resources: servers and network links. Server resource allocation problem is the problem of how to allocate virtual machines (VMs) to physical machines (PMs). By modeling server resources (CPU, memory, storage, IO, etc.) as a multidimensional vector space, we present design criteria for metrics that measure the fitness of an allocation of VMs into PMs. We propose two novel metrics that conform to these design criteria. We also propose VM allocation methods that use these metrics to compare allocation alternatives when allocating a set of VMs into a set of PMs. We compare performances of our proposed metrics to the ones from the literature using vector bin packing with heterogeneous bins (VBPHB) benchmark. Results show that our methods find feasible solutions to a greater number of allocation problems than the others. Network resource allocation problem is examined in hybrid wireless data centers. We propose a system model in which each top-of-the-rack (ToR) switch is equipped with two radios operating in 60-GHz band using 3-channel 802.11ad. Given traffic flows between servers, we allocate wireless links between ToR switches so that the traffic carried over the wireless network is maximized. We also present a method to randomly generate traffic based on a real data center traffic pattern. We evaluate the performance of our proposed traffic allocation methods using randomly generated traffic. Results show that our methods can offload significant amount of traffic from wired to wireless network, while achieving low latency, high throughput, and high bandwidth utilization.