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It is well known that Max-Weight type scheduling algorithms are throughput optimal since they achieve the maximum throughput while maintaining the network stability. However, the majority of existing works employing Max-Weight algorithm require the complete channel state information (CSI) at the scheduler without taking into account the associated overhead. In this work, we design a Scheduling and Selective Feedback algorithm (SSF) taking into account the overhead due to acquisition of CSI. SSF algorithm collects CSI from only those users with sufficiently good channel quality so that it always schedules the user with the highest queue backlog and channel rate product at every slot. We characterize the achievable rate region of SSF algorithm by showing that SSF supports 1 + ϵ fraction of the rate region when CSI from all users are collected. We also show that the value of ϵ depends on the expected number of users which do not send back their CSI to the base station. For homogenous and heterogeneous channel conditions, we determine the minimum number of users that must be present in the network so that the rate region is expanded, i.e., ϵ > 0. We also demonstrate numerically in a realistic simulation setting that this rate region can be achieved by collecting CSI from only less than 50% of all users in a CDMA based cellular network utilizing high data rate (HDR) protocol.