Novel Vector Packing Heuristic for VM Placement Based on the Divide-and-Conquer Paradigm

VM Placement algorithms play a crucial role in determining data center utilisation and power consumption. The problem of VM Placement is to obtain an optimal packing of VMs on hosts such that the number of hosts required is minimum. The problem being NP-Hard, it becomes practically infeasible to get an optimal placement within the time constraints for making scheduling decisions. VM Placement can be modeled as a Multi-dimensional Vector Packing Problem(MDVPP). VPSolver, using arc-flow formulation with graph compression, gives an optimal solution for Bin-Packing and related problems. This paper proposes heuristics for large instances of MDVPP, based on the Divide-and-Conquer paradigm, using VPSolver. An extensive evaluation, with 3260 instances, comparing our heuristic with existing popular heuristics in 2D and 3D vector spaces is done which also includes VM Sizes obtained from utilisation traces of a private cloud. It is observed that for most large instances, our heuristic gives better solutions compared to existing methods sometimes at the cost of higher computation time taken. The proposed heuristic gives solutions where the number of bins required is reduced up to 7.34% and 8.15% for 2D and 3D vector spaces respectively.