Virtual Network Embedding Through Graph Eigenspace Alignment

Abstract

The purpose of this paper is to study tradeoffs between efficiency and precision for the general virtual network embedding (VNE) problem. To narrow the gap between solutions contributed by previous heuristic schemes and the optimal solution, and to ease the unacceptable computational burden of optimization approaches to VNE for large-scale networks, we propose the use of graph eigenspace notions for node mapping, that is, for associating virtual nodes to substrate nodes (SNs). We also contribute an inexact algorithm which projects all SNs to a 2-D eigenspace for generating a more efficient node mapping. There are some similarities between our method and numerous graph-matching strategies emerging in machine learning fields, but there are also some differences between the two, because the VNE problem is not strictly mathematical with respect to the mapping it seeks. Thus, we provide the relevant theoretical evidence to guarantee the solution quality of our scheme compared with a couple of previous VNE proposals. Simulation results demonstrate that our schemes can reach a better tradeoff point regarding runtime (that approaches the overhead of implementing eigendecomposition of a general matrix) and embedding quality metrics. Besides, our inexact algorithm using 2-D projection exhibits an improvement in quality over previous node-rank-based methods.