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Compared with a bufferless crossbar switch, a combined input-crosspoint-queued (CICQ) switch has better scalability owing to its distributed scheduling. Although the previously proposed round-robin algorithms achieve 100% throughput asymptotically under uniform traffic, these algorithms do not provide a satisfactory performance under nonuniform traffic. In this paper, we propose an efficient round-robin algorithm for a CICQ switch with one-cell cross point buffers. With our algorithm, each input arbiter is associated with dual round-robin pointers. Unlike the existing round-robin algorithms, our algorithm has distinctive round-robin pointer updating rules which are powerful to cope with nonuniform traffic patterns. Extensive simulation results show that our algorithm achieves a satisfactory performance under both uniform and a broad class of nonuniform traffic patterns.