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In this paper, we deal with the time slot allocation in time-hopping ultra-wide band (TH-UWB) ad-hoc networks in order to maximize the total sum rate. This problem is known to be a discrete NP-hard optimization problem and hence cannot be solved with a computationally efficient algorithm. Moreover, the sum rate maximization often leads to starvation of links experiencing bad channel conditions. Our main contribution is to propose an algorithm which approaches the maximum sum rate while keeping the starvation rate under a threshold. We first propose a time slot allocation scheme based on an accept/reject criterion. The performance of the algorithm depends on the acceptance threshold. In a second approach, we add the starvation rate in constraints leading to a new algorithm maximizing the sum rate and keeping the starvation rate under control. Extensive simulation results show that the proposed algorithm achieves reasonable sum rate performances under restrictive starvation threshold.