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The problem of multi-rate power-controlled collision-free scheduling in spatial time division multiple access (STDMA) wireless mesh networks is formulated as a mathematical program utilising cross layer information. As these mixed integer linear programs are intractable (NP-hard problems), optimal collision-free schedules can be found only for topologies consisting of a few nodes. To this end, approximation algorithms that are based on linear programming relaxation and randomised rounding are studied. The proposed framework, which aims to maximise the spatial timeslot reuse under predefined signal-to-interference noise ratio thresholds, is suitable for providing centralised scheduling in the mesh mode of the IEEE 802.16 standard. Performance aspects of the approximation algorithms under different scenarios are investigated.