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Future broadband communication networks are expected to be OFDMA-based with generic ad hoc topologies, wherein the wireless nodes play multiple roles, including transmission, reception and relaying. When the schedules by which the OFDMA subchannels are assigned to wireless links are binary, obtaining a characterization of the maximum rates that can be reliably communicated by these networks can be shown to be NP-hard. To circumvent this difficulty, we provide efficient means for computing two lower bounds on the achievable weighted sum rates. The first bound is obtained by using geometric programming approximation techniques, whereas the second bound is obtained by rounding the solutions of a relaxed version of the cross layer design problem. Finally, we consider an existing upper bound on the achievable weighted sum rates, and we use numerical simulations to show that the lower and upper bounds are relatively tight, especially at high signal-to-noise ratios.