On the Virtual Network Embedding polytope
🤖 AI Summary
This study addresses the computational inefficiency of integer programming approaches for virtual network embedding (VNE) by conducting the first polyhedral analysis of the VNE problem. The authors introduce novel valid inequalities that precisely characterize the embedding structure of virtual links over substrate paths. By integrating flow decomposition algorithms with polyhedral theory, they strengthen the formulation of the mixed-integer programming (MIP) model, enhancing its tightness. Experimental results demonstrate that the proposed inequalities significantly accelerate the convergence of MIP solvers while preserving solution quality, thereby offering both theoretical insights and practical tools for the exact solution of VNE problems.
Application Category
📝 Abstract
We initiate the polyhedral study of the Virtual Network Embedding (VNE) problem, which arises in modern telecommunication networks. We propose new valid inequalities for the so-called flow formulation. We then prove, through a dedicated flow decomposition algorithm, that these inequalities characterize the VNE polytope in the case of an embedding of a virtual edge on a substrate path. Preliminary experiments show that the new inequalities propose promising speedups for MIP solvers.
Problem
Research questions and friction points this paper is trying to address.
Virtual Network Embedding
polytope
telecommunication networks
flow formulation
valid inequalities
Innovation
Methods, ideas, or system contributions that make the work stand out.
Virtual Network Embedding
polyhedral study
valid inequalities
flow decomposition
MIP acceleration
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