We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V,E) with nonnegative edge weight d(u,v), (u,v) in E, and two integers K and B, find a partition of the nodes of G into K subsets so that the total weight of the edges connecting the nodes in different subsets of the partition is minimized and the total weight of the edges incident to any subset of the partition is at most B. This problem, called the K-SONET Ring Assignment Problem (K-SRAP), arises in the design of optical telecommunication networks when a ring-based topology is adopted. We show that this network topology problem corresponds to a graph partitioning problem with capacity constraints and it is NP-hard. In this paper we propose a novel and compact 0-1 integer linear programming formulation for this problem. We report computational results comparing our formulation with another formulation found in the literature. The results show that our formulation outperforms the previous one.

## Citation

AT&T Labs Research Technical Report TD-6HLLNR, October 28, 2005.

## Article

View A novel integer programming formulation for the K-SONET ring assignment problem