The paper is devoted to modeling and optimization\nof reliable wireless mesh networks that employ directional\nantennas. We introduce two mixed-integer programming\nformulations that allow to simultaneously characterize\nrouting patterns and transmission schedules. The first model\nallows for maximizing the minimal flow in a network. The\nsecond model involves reliability constraints and aims at\nminimizing the number of used directional antennas. In both\ncases locations of mesh routers are known. However, the\nnumber of installed radio interfaces and their directions are\nsubject to optimization. We discuss a way of solving a cost\nminimization problem based on the introduced characterization,\nand present an extensive numerical study that illustrates\nthe efficiency of the solution algorithm. We also provide an\nalgorithm capable of verifying feasibility of obtained solutions.\nMoreover, in rare cases of failed verification, the algorithm\nprovides additional constraints that should be added to\nthe problem.
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