Virtual network mapping (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 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 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.
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