This work presents a new optimization framework for cellular networks using neighborhood-based optimization. Under this optimization framework, resources are allocated within virtual cells encompassing several base-stations and the users within their coverage areas. We form the virtual cells using hierarchical clustering with a minimax linkage criterion given a particular number of such cells. Once the virtual cells are formed, we consider a single-user detection interference coordination model in which base-stations in a virtual cell jointly allocate the channels and power to users within the virtual cell. We propose two new schemes for solving this mixed integer NP- hard resource allocation problem. The first scheme transforms the problem into a continuous variables problem; the second scheme proposes a new channel allocation method and then alternately solves the channel allocation problem using this new method, and the power allocation problem. We evaluate the average system sum rate of these schemes for a variable number of virtual cells. These results quantify the sum-rate along a continuum of fully- centralized versus fully-distributed optimization for different clustering and resource allocation strategies. These results indicate that the penalty of fully-distributed optimization versus fully-centralized (cloud RAN) can be as high as 50%. However, if designed properly, a few base stations within a virtual cell using neighborhood- based optimization have almost the same performance as fully-centralized optimization.