Cloud systems empower the big data management by providing virtual machines (VMs) to process data nodes (DNs) in a faster, cheaper and more effective way. The efficiency of a VM allocation is an important concern that is influenced by the communication latencies. In the literature, it has been proved that the VM assignment minimizing communication latency in the presence of the triangle inequality is 2-approximation. However, a 2-approximation solution is not efficient enough as data center networks are not limited to the triangle inequality. In this paper, we define the quadrilateral inequality property for latencies such that the time complexity of the VM assignment problem minimizing communication latency in the presence of the quadrilateral inequality is in P (polynomial) class. Indeed, we propose an algorithm for the problem of assigning VMs to DNs to minimize the maximum latency among allocated VMs in addition to DNs with their assigned VMs. This algorithm is latency optimal and 2-approximation for networks with the quadrilateral inequality and the triangle inequality, respectively. Besides, the extension of the proposed method can be applied to the cloud elasticity. The simulation results illustrate the good performance and scalability of our method in various known data center networks.

中文翻译：

---

最小化云系统中虚拟机分配的数据访问延迟

云系统通过提供虚拟机 (VM) 以更快、更便宜和更有效的方式处理数据节点 (DN)，从而为大数据管理提供支持。VM 分配的效率是受通信延迟影响的一个重要问题。在文献中，已经证明在存在三角不等式的情况下最小化通信延迟的 VM 分配是 2-近似。然而，由于数据中心网络不限于三角不等式，因此 2 近似解决方案不够有效。在本文中，我们定义了延迟的四边形不等式属性，使得在存在四边形不等式的情况下最小化通信延迟的 VM 分配问题的时间复杂度为 P（多项式）类。确实，我们针对将 VM 分配给 DN 的问题提出了一种算法，以最小化分配的 VM 之间的最大延迟以及分配有 VM 的 DN。对于分别具有四边形不等式和三角不等式的网络，该算法是延迟最优和 2-近似。此外，所提出的方法的扩展可以应用于云弹性。仿真结果说明了我们的方法在各种已知数据中心网络中的良好性能和可扩展性。