We present new lower bounds for the size of perfect and separating hashfamilies ensuring their existence. Such new bounds are based on the algorithmicCluster expansion improved version of the Lov\'asz Local Lemma, which alsoimplies that the Moser-Tardos algorithm finds such hash families in polynomialtime.
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机译:我们为完善和分离的哈希家族的大小提供了新的下界,以确保它们的存在。这样的新边界基于Lov'asz Local Lemma的algorithmCluster扩展改进版本,这也意味着Moser-Tardos算法在多项式时间内找到了此类哈希族。
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