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In this work, we consider the problem of maximizing the reliability of connections in mesh networks against failure scenarios in which multiple links may fail simultaneously. We consider the single-path connection problem as well as multiple-path (protected) connection problems. The problems are formulated as minimum-color path problems, where each link is associated with one or more colors, and each color corresponds to a given failure event Thus, when a certain color fails, all links which include that color will fail. In a single-path problem, by minimizing the number of colors on the path, the failure probability of the path can be minimized if all colors have the same probability of causing failures. In the case of two paths, where one path is a protection path, if all colors have the same probability of causing failures, the problem becomes that of finding two link-disjoint paths which either have a minimum total number …