Virtual Network Mapping: A Graph Pattern Matching Approach

Abstract

Virtual network mapping ($\mathsf {VNM}$) is to build a network on demand by deploying virtual machines in a substrate network, subject to constraints on capacity, bandwidth and latency. It is critical to data centers for coping with dynamic cloud workloads. This paper shows that $\mathsf {VNM}$ can be approached by graph pattern matching, a well-studied database topic. (1) We propose to model a virtual network request as a graph pattern carrying various constraints, and treat a substrate network as a graph in which nodes and edges bear attributes specifying their capacity. (2) We show that a variety of mapping requirements can be expressed in this model, such as virtual machine placement, network embedding and priority mapping. (3) In this model, we formulate $\mathsf {VNM}$ and its optimization problem with a mapping cost function. We establish complexity bounds of these problems for various mapping constraints, ranging from PTIME to NP-complete. For intractable optimization problems, we further show that these problems are approximation-hard, i.e., NPO-complete in general and APX-hard even for special cases.