Internet traffic has increased at a very fast pace in recent years. The traffic demand requires that future packet switching systems should be able to switch packets in a very short time, i.e., just a few nanoseconds. Algorithms with lower computation complexity are more desirable for this high-speed switching design. Among the existing algorithms that can achieve 100% throughut for input-queued switches for any admissible Bernoulli traffic, ALGO3  and EMHW  have the lowest computation complexity, which is O(logN), where N is the number of ports in the switch. In this paper, we propose a randomized scheduling algorithm, which can also stabilize the system for any admissible traffic that satisfies the strong law of large number. The algorithm has a complexity of O(1). Since the complexity does not increase with the size of a switch, the algorithm is highly scalable and a good choice for future high-speed switch designs. We also show that the algorithm can be implemented in a distributed way by using a low-rate control channel. Simulation results show that the algorithm can provide a good delay performance as compared to algorithms with higher computation complexity.