Seed explosion is a fundamental problem in fuzzing seed scheduling, where a fuzzer maintains a huge corpus and fails to choose promising seeds. Existing works focus on seed prioritization but still suffer from seed explosion since corpus size remains huge. We tackle this from a new perspective: corpus reduction, i.e., computing a seed corpus subset. However, corpus reduction could lead to poor seed diversity and large runtime overhead. Prior techniques like cull_queue, AFL-Cmin, and MinSet suffer from poor diversity or prohibitive overhead, making them unsuitable for high-frequency seed scheduling. We propose RandSet, a novel randomized corpus reduction technique that reduces corpus size and yields diverse seed selection simultaneously with minimal overhead. Our key insight is introducing randomness into corpus reduction to enjoy two benefits of a randomized algorithm: randomized output (diverse seed selection) and low runtime cost. Specifically, we formulate corpus reduction as a set cover problem and compute a randomized subset covering all features of the entire corpus. We then schedule seeds from this small, randomized subset rather than the entire corpus, effectively mitigating seed explosion. We implement RandSet on three popular fuzzers: AFL++, LibAFL, and Centipede, and evaluate it on standalone programs, FuzzBench, and Magma. Results show RandSet achieves significantly more diverse seed selection than other reduction techniques, with average subset ratios of 4.03% and 5.99% on standalone and FuzzBench programs. RandSet achieves a 16.58% coverage gain on standalone programs and up to 3.57% on FuzzBench in AFL++, triggers up to 7 more ground-truth bugs than the state-of-the-art on Magma, while introducing only 1.17%-3.93% overhead.