A decomposition approach for large virtual network embedding

2025-12-19

AI Summary

Virtual Network Embedding (VNE) is a core optimization problem in 5G network slicing, requiring joint node mapping and link routing onto a shared substrate network to minimize cost while ensuring feasibility. Existing heuristic approaches often fail or yield low-quality solutions under large-scale, resource-constrained conditions. This paper proposes an integer linear programming (ILP) decomposition framework based on automated virtual network partitioning. The original VNE problem is reformulated as a hierarchical column generation structure, where both the master problem and subproblem are themselves VNE instances. We further design an efficient Price-and-Branch heuristic to solve the decomposed formulation. Evaluated on real-world large-scale topology benchmarks, our method significantly improves the quality of lower bounds, solution success rate, and economic efficiency (i.e., embedding cost). Notably, it consistently produces feasible solutions even under sparse-resource scenarios—outperforming the current state-of-the-art heuristics.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Optimizes virtual network embedding for 5G network slicing
• Addresses high-cost and failure issues in large-scale VNE
• Proposes decomposition and column generation for improved solutions

Innovation

• Decomposes virtual networks via automatic partitioning
• Uses column generation with VNE pricing subproblems
• Implements Price-and-Branch heuristic for large instances