arXiv subjects

Alexis Schneider

Publications and source records attributed to Alexis Schneider.

3 recordsLinked to original sources

arXiv2026

On the Virtual Network Embedding polytope

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.

cs.DM↗

arXiv2025

A decomposition approach for large virtual network embedding

Virtual Network Embedding (VNE) is the core combinatorial problem of Network Slicing, a 5G technology which enables telecommunication operators to propose diverse service-dedicated virtual networks, embedded onto a common substrate network. VNE asks for a minimum-cost mapping of a virtual network on a substrate network, encompassing simultaneous node placement and edge routing decisions. On a benchmark of large virtual networks with realistic topologies we compiled, the state-of-the art heuristics often provide expensive solutions, or even fail to find a solution when resources are sparse. We introduce a new integer linear formulation together with a decomposition scheme based on an automatic partition of the virtual network. This results in a column generation approach whose pricing problems are also VNE problems. This method allows to compute better lower bounds than state-of-the-art methods. Finally, we devise an efficient Price-and-Branch heuristic for large instances.

cs.DM↗

arXiv2025

Complexity of the Virtual Network Embedding with uniform demands

We study the complexity of the Virtual Network Embedding Problem (VNE), which is the combinatorial core of several telecommunication problems related to the implementation of virtualization technologies, such as Network Slicing. VNE is to find an optimal assignment of virtual demands to physical resources, encompassing simultaneous placement and routing decisions. The problem is known to be strongly NP-hard, even when the virtual network is a uniform path, but is polynomial in some practical cases. This article aims to draw a cohesive frontier between easy and hard instances for VNE. For this purpose, we consider uniform demands to focus on structural aspects, rather than packing ones. To this end, specific topologies are studied for both virtual and physical networks that arise in practice, such as trees, cycles, wheels and cliques. Some polynomial greedy or dynamic programming algorithms are proposed, when the physical network is a tree or a cycle, whereas other close cases are shown NP-hard.

cs.DM↗