We propose a novel job scheduling approach for homogeneous cluster computing platforms. Its key feature is the use of virtual machine technology for sharing resources in a precise and controlled manner. We justify our approach and propose several job scheduling algorithms. We present results obtained in simulations for synthetic and real-world High Performance Computing (HPC) workloads, in which we compare our proposed algorithms with standard batch scheduling algorithms. We find that our approach widely outperforms batch scheduling. We also identify a few promising algorithms that perform well across most experimental scenarios. Our results demonstrate that virtualization technology coupled with lightweight scheduling strategies affords dramatic improvements in performance for HPC workloads.