Designing Hypergraph Layouts to GMPLS Routing Strategies

Abstract

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the problem by associating to each routing strategy a logical hypergraph whose hyperarcs are dipaths of the physical graph, called tunnels in GMPLS terminology. Such a hypergraph is called a hypergraph layout, to which we assign a cost function given by its physical length plus the total number of hops traveled by the traffic. Minimizing the cost of the design of an AOLS network can then be expressed as finding a minimum cost hypergraph layout.

We prove hardness results for the problem, namely for general directed networks we prove that it is NP-hard to find a C logn-approximation, where C is a a positive constant and n is the number of nodes of the network. For symmetric directed networks, we prove that the problem is APX-hard. These hardness results hold even is the traffic instance is a partial broadcast. On the other hand, we provide an $\mathcal{O}(\log n)$-approximation algorithm to the problem for a general symmetric network. Finally, we focus on the case where the physical network is a path, providing a polynomial-time dynamic programming algorithm for a bounded number of sources, thus extending the algorithm given in [1] for a single source.

This work has been partly funded by the European project IST FET AEOLUS and the project “Optimization Models for NGI Core Network” (Polish Ministry of Science and Higher Education, grant N517 397334).