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Appropriate use of randomness in the development of scheduling algorithms is a powerful tool, because it leads to systems that are theoretically efficient and fair, while feasible to analyze and obtain concrete performance bounds. However, randomness is hard to implement, due to the high complexity and long delay of efficient random number generators. Thus, deterministic schedulers for high-speed switches have been developed. In this paper, we introduce high-speed schedulers for packet switches, which employ randomness and provide high performance at low cost. The schedulers implement variations of an existing, optimal on-line bipartite graph matching algorithm and achieve fair service and improved performance over PIM at a significantly lower cost; PIM is the main alternative algorithm with random decisions and has been used as the basis for a wide range of deterministic algorithms.