2000年台湾大专题。。。英语阅读输入输出专场。。我只能说很强势。。

M. Frequent Subsets Problem

The frequent subset problem is defined as follows. Suppose UU={1, 2,\ldots…,N} is the universe, and S_{1}S1​​, S_{2}S2​​,\ldots…,S_{M}SM​​ are MM sets over UU. Given a positive constant \alphaα, 0<\alpha \leq 10<α1, a subset BB (B \neq 0B0) is α-frequent if it is contained in at least \alpha MαM sets of S_{1}S1​​, S_{2}S2​​,\ldots…,S_{M}SM​​, i.e. \left | \left \{ i:B\subseteq S_{i} \right \} \right | \geq \alpha M{i:BSi​​}αM. The frequent subset problem is to find all the subsets that are α-frequent. For example, let U=\{1, 2,3,4,5\}U={1,2,3,4,5}, M=3M=3, \alpha =0.5α

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