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Service restoration and survivability have become increasingly important in telecommunications network planning with the introduction of fiber-optic high-speed networks. Synchronous optical network (SONET) technology promotes the use of interconnected rings in designing reliable networks. We describe a heuristic approach for designing networks comprised of interconnected rings. Our approach is particularly attractive for relatively sparse networks in which the set of all cycles (constituting the potential rings) can be determined at a reasonable computational effort. Most networks fall into this category. Given a set of nodes, with demand among all possible node-pairs, and a set of available links that connect the nodes, the problem is to select an optimal subset of rings, utilizing only allowable links, such that each node is included in at least one ring and each ring is connected to at least one other ring at two or more nodes. Such a multiple ring network ensures instantaneous restoration of service in case of a single link or node failure. We first generate a large set of candidate rings and approximate the cost of each ring based on the nodes that are served by the ring and based on the demands. We then apply a set covering algorithm that selects a (minimum cost) subset of the candidate rings such that each node is included on at least one ring. Finally, we select a few additional rings in order to achieve the required connectivity among the rings. We present computational results for realistic-size (e.g., 500 nodes) telecommunication networks