Large-scale data analytics frameworks are shifting towards shorter task durations and larger degrees of parallelism to provide low latency. Scheduling highly parallel jobs that complete in hundreds of milliseconds poses a major challenge for task schedulers, which will need to schedule millions of tasks per second on appropriate machines while offering millisecond-level latency and high availability. We demonstrate that a decentralized, randomized sampling approach provides near-optimal performance while avoiding the throughput and availability limitations of a centralized design. We implement and deploy our scheduler, Sparrow, on a 110-machine cluster and demonstrate that Sparrow performs within 12% of an ideal scheduler. In the ACM Digital Library: http://dl.acm.org/citation.cfm?id=2522716