The complexity of the overlay network verification and its related problems

In this paper we introduce a special type of virtual networks called an overlay network. We first study a decision problem called the Overlay Network Verification Problem and show that this problem is NP-complete. We then place some restriction to the original problem and prove that the Overlay Network Verification Problem still remains NP-complete. A similar problem called the Two-Label Overlay Network Verification Problem is then investigated. The complexities of this problem and its variant are then discussed. A list of open problems and the real-world applications of our results are given in the conclusion.