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To enable the rapid execution of many tasks on compute clusters, we have developed Falkon, a Fast and Light-weight tasK executiON framework. Falkon integrates (1) multi-level scheduling to separate resource acquisition (via, e.g., requests to batch schedulers) from task dispatch, and (2) a streamlined dispatcher. Falkon's integration of multi-level scheduling and streamlined dispatchers delivers performance not provided by any other system. We describe Falkon architecture and implementation, and present performance results for both microbenchmarks and applications. Microbenchmarks show that Falkon throughput (487 tasks/sec) and scalability (to 54,000 executors and 2,000,000 tasks processed in just 112 minutes) are one to two orders of magnitude better than other systems used in production Grids. Large-scale astronomy and medical applications executed under Falkon by the Swift parallel programming system achieve up to 90% reduction in end-to-end run time, relative to versions that execute tasks via separate scheduler submissions.