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This paper presents a randomized algorithm, called degree-sequenced matching (DSM), for scheduling packets in an input-queued switch. Previously known high-throughput, randomized algorithms implicitly prioritize the matching of ports with larger degrees and causes longer delays at the low-degree ports. Our algorithm, however, achieves a lower average delay but without compromising the throughput. The DSM algorithm sorts nodes based on their node-degrees and begin each iteration of the algorithm by matching the lowest degree nodes. Using real gateway traffic traces as well as synthetically generated traffic, we present simulation results showing that DSM achieves a low average delay, while still achieving near maximum throughput.