It has recently been shown that a combined input and output queued (CIOQ) switch with a speed-up factor of 2 can exactly emulate an output-queued (OQ) switch. The main benefit of using a CIOQ switch is to reduce memory bandwidth requirement while providing quality of service (QoS) guarantee. The key component for exact emulation is a matching algorithm for bipartite graphs. For example, a CIOQ switch with a speed-up factor of 2, which adopts the least cushion first/most urgent first (LCF/MUF) matching algorithm, can exactly emulate an OQ switch with any arbitrary service discipline. However, the complexities of cushion calculation and cell reordering required at the output ports make the algorithm very difficult to be realised in a high-speed switch. The authors propose an approximate LCF/MUF algorithm and evaluate its performance for the weighted round-robin service discipline. For ease of implementation, the proposed algorithm calculates approximate cushions and does not perform reordering at the output ports. The trade-off is that it loses the property of exact emulation. It was found, via computer simulations, that the performance of a CIOQ switch with the proposed single-iteration matching algorithm is close to that of an OQ switch under uniform, nonuniform, and correlated input traffic models for offered load up to 0.9. In addition, the cell departure order can be maintained under the single-iteration algorithm.