For cloud data center, Virtual Machine (VM) consolidation is an effective way to save energy and improve efficiency. However, inappropriate consolidation of VMs, especially aggressive consolidation, can lead to performance problems, and even more serious Service Level Agreement (SLA) violations. Therefore, it is very important to solve the tradeoff between reduction in energy use and reduction of SLA violation level. In this paper, we propose two Host State Detection algorithms and an improved VM placement algorithm based on our proposed Host State Binary Decision Tree Prediction model for SLA-aware and energy-efficient consolidation of VMs in cloud data centers. We propose two formulas of conditions for host state estimate, and our model uses them to build a Binary Decision Tree manually for host state detection. We extend Cloudsim simulator to evaluate our algorithms by using PlanetLab workload and random workload. The experimental results show that our proposed model can significantly reduce SLA violation rates while keeping energy cost efficient, it can reduce the metric of SLAV by at most 98.12% and the metric of Energy by at most 33.96% for real world workload.

A tree-shellable function is a positive Boolean function which can be represented by a binary decision tree whose number of paths from the root to a leaf labeled 1 equals the number of prime implicants. In this paper, we consider the tree-shellability of DNFs with restrictions. We show that, for read-k DNFs, the number of terms in a tree-shellable function is at most k2. We also show that, for k-DNFs, recognition of ordered tree-shellable functions is NP-complete for k=4 and tree-shellable functions can be recognized in polynomial time for constant k.