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We study the diverse routing problem in optical mesh networks. We use a general framework based on shared risk link groups to model the problem. We prove that the diverse routing problem is indeed NP-complete, a result that has been conjectured by several researchers previously. In fact, we show that even the fiber-span-disjoint paths problem, a special case of the diverse routing problem, is also NP-complete. We then develop an integer linear programming formulation and show through numerical results that it is a very viable method to solve the diverse routing problem for most optical networks found in many applications which typically have no more than a few hundred nodes and fiber spans.