On the Virtual Network Embedding polytope

TL;DR

This paper introduces a polyhedral approach to the Virtual Network Embedding problem, proposing new inequalities that improve solving efficiency for specific cases and advancing the mathematical understanding of VNE.

Contribution

It develops new valid inequalities for the VNE polytope and demonstrates their effectiveness in speeding up MIP solvers for certain embeddings.

Findings

New inequalities characterize the VNE polytope for virtual edge embeddings on substrate paths.

Preliminary experiments show promising speedups in MIP solving.

The flow decomposition algorithm aids in polyhedral characterization.

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.