The design of logical topologies in wavelength-routing multihop optical networks is a well-studied problem. In this paper, we consider logical topology (LT) design over the popular ring and linear topologies. Our objective is the minimization of the electronic processing delay for the worst case traffic flow. For uniform traffic between nodes, this delay minimization corresponds to minimizing the number of hops on a shortest path between the farthest two nodes in the logical topology (the

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... er of the logical topology). The simple structure of the physical topologies enables us to present a rigorous analysis of the problem. We present lower bounds for the achievable diameter wherever possible and propose practical logical topology design algorithms and corresponding upper bounds. We also present an application of the LT designs in the linear topology to the survivability of ring networks.