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This letter introduces a centralized joint power and admission control algorithm for cognitive radio networks. Its novelty lies in the proposed admission metric. Unlike those in existing algorithms, our metric predetermines the admission order of N secondary users which intend to access the network. This allows us to search a group of admitted secondary users with the bisection method. The proposed algorithm is shown by simulation to achieve a comparable performance to existing algorithms, and the computational complexity is reduced from O(N3) to O(N2 log2 N).