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}SMare MM sets over UU. Given a positive constant \alphaα, 0<\alpha \leq 10<α≤1, a subset BB (B \neq 0B≠0) 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:B⊆Si}∣≥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,

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