Optimal Virtual Network Embeddings for Tree Topologies

TL;DR

This paper presents the first fixed-parameter algorithm for the NP-hard Virtual Network Embedding Problem on tree topologies, significantly improving computational efficiency and enabling optimal solutions in practical scenarios.

Contribution

It introduces a novel fixed-parameter algorithm for the VNEP on tree topologies, with substantial speed improvements over existing methods.

Findings

Algorithm achieves over 200x faster runtimes than integer programming methods.

Provides the first fixed-parameter algorithm for VNEP on tree topologies.

Includes hardness results for the VNEP and related problems.

Abstract

The performance of distributed and data-centric applications often critically depends on the interconnecting network. Applications are hence modeled as virtual networks, also accounting for resource demands on links. At the heart of provisioning such virtual networks lies the NP-hard Virtual Network Embedding Problem (VNEP): how to jointly map the virtual nodes and links onto a physical substrate network at minimum cost while obeying capacities. This paper studies the VNEP in the light of parameterized complexity. We focus on tree topology substrates, a case often encountered in practice and for which the VNEP remains NP-hard. We provide the first fixed-parameter algorithm for the VNEP with running time $O(3^r (s+r^2))$ for requests and substrates of $r$ and $s$ nodes, respectively. In a computational study our algorithm yields running time improvements in excess of 200x compared to state-of-the-art integer programming approaches. This makes it comparable in speed to the well-established ViNE heuristic while providing optimal solutions. We complement our algorithmic study with hardness results for the VNEP and related problems.