High-aggregate bandwidth switches are those whose port count multiplied by the operating line rate is very high; for example, a 30 port switch operating at 40 Gbps or a 1000 port switch operating at 1 Gbps. Designing high-performance schedulers for such switches is challenging for the following reasons: (i) high performance requires finding good matchings; (ii) good matchings take time to find; (iii) in high-aggregate bandwidth switches there is either too little time (due to high line rates) or there is too much work to do (due to a high port count). We exploit the following features of the switching problem to devise simple-to-implement, high-performance schedulers: (a) the state of the switch (carried in the lengths of its queues) changes slowly with time, implying that heavy matchings will likely stay heavy over a period of time; (b) observing arriving packets conveys useful information about the state of the switch. These features are exploited using hardware parallelism and randomization to yield three scheduling algorithms for IQ (input-queued) switches – APSARA, LAURA and SERENA. These algorithms are shown to achieve 100% throughput and simulations show that their delay performance is quite competitive with respect to the maximum weight matching. The stability proof involves a derandomization procedure and uses methods which may have wider applicability.