We consider the problem of placing virtual clusters, each consisting of a set of heterogeneous virtual machines (VM) with some interrelationships due to communication needs and other dependability-induced constraints, onto physical machines (PM) in a large data center. The placement of such constrained, networked virtual clusters, including compute, storage, and networking resources is challenging. The size of the problem forces one to resort to approximate and heuristics-based optimization techniques. We introduce a statistical approach based on importance sampling (also known as cross-entropy) to solve this placement problem. A straightforward implementation of such a technique proves inefficient. We considerably enhance the method by biasing the sampling process to incorporate communication needs and other constraints of requests to yield an efficient algorithm that is linear in the size of the data center. We investigate the quality of the results of using our algorithm on a simulated system, where we study the effects of various parameters on the solution and performance of the algorithm. © 2012 IEEE.