Domain clustering for inter-domain path computation speed-up

We consider a multi-domain network scenario and we study the Inter-Domain Path Computation problem under the Domain Uniqueness constraint (IDPC-DU), that is, a path cannot visit a domain twice. It is known that hierarchical Path Computation Element (h-PCE) architecture, that is commonly used to solve IDPC-DU, shows poor scalability with respect to the number of domains. For this reason, we devise a new domain clustering concept allowing one to artificially reduce the number of domains in an offline phase, in order to solve IDPC-DU with lower complexity at run-time. More specifically, we first prove the NP-completeness of the feasibility problem associated with IDPC-DU and the inapproximability of IDPC-DU itself. Yet, we show that the number of domains is the real computational bottleneck for the solution of IDPC-DU. Then we provide a necessary and sufficient condition for a domain clustering to be proper, that is, without loss of optimality. Such a condition can be verified offline on the inter-domain graph. We finally show via numerical experiments the impact of the inter-domain treewidth on the computational speed-up brought by proper clustering.