Apriori Property and Breadth-First Search Algorithms
Downward closure property; Levelwise search; Monotonicity property
Given a large database of sets of items, called transactions, the goal of frequent itemset mining is to find all subsets of items, called itemsets, occurring frequently in the database, i.e., occurring in a given minimum number of transactions.
The search space of all itemsets is exponential in the number of different items occurring in the database. Hence, the naive approach to generate and count the frequency of all itemsets over the database can not be achieved within reasonable time. Also, the given databases could be massive, containing millions of transactions, making frequency counting a tough problem in itself.
Therefore, numerous solutions have been proposed to perform a more directed search through the search space, almost all relying on the well known Apriori-property. These solutions can be divided into breadth-first search and depth-first search, of which the first is discussed here.
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