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We consider the problem of scheduling a user in a multi-user wireless environment in a distributed manner. The opportunistic splitting algorithm is applied to find the best group of users without reporting the channel state information to the centralized scheduler. The users find the best among themselves while requiring just a ternary feedback from the common receiver at the end of each mini-slot. The original splitting algorithm is modified to handle users with asymmetric channel conditions. We use a score-based approach with the splitting algorithm to introduce time and throughput fairness while exploiting the multi-user diversity of the network. Analytical and simulation results are given to show that the modified score-based splitting algorithm works well as a fair scheduling scheme with good spectral efficiency and reduced feedback.