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.

翻译：虚拟网络嵌入（VNE）是网络切片这一5G技术的核心组合优化问题，该技术使电信运营商能够在公共底层网络上部署多种服务专用的虚拟网络。VNE要求在满足节点放置与边路由同时决策的条件下，将虚拟网络以最小成本映射到底层网络。在我们构建的具有现实拓扑结构的大规模虚拟网络基准测试中，现有启发式算法通常只能提供高成本解，甚至在资源稀缺时无法找到可行解。本文提出了一种新的整数线性规划模型，并结合基于虚拟网络自动划分的分解策略。该方法形成了列生成算法，其定价问题本身也是VNE问题。该算法能计算出比现有方法更优的下界。最后，我们设计了一种针对大规模实例的高效定价分支启发式算法。