Telecommunication Clustering using Linear and Semide nite

Recent advances in optical ber systems and transmission equipments play a primary role in today's telecommunications networks. The standardized SDH (Synchronous Digital Hierarchy) technology made the rings the most survivable architecture for designing high speed networks. Designing such networks involves not only the connguration of rings at the logical level but also the mapping of such conngurations on the physical level, i.e. ber paths. This paper deals with the problem of nding optimal clusters of nodes to be used as the basis for designing logical rings. In the simplest form, this problem is equivalent to k-equipartition, and can be modeled as a quadratic pseudo-boolean problem. We consider both linear and semideenite relaxations and present numerical results on real data from France Telecom networks with up 900 nodes, and also on randomly generated problems.