  In order to generate synthetic basket data sets for better benchmark testing,
it is important to integrate characteristics from real-life databases into the
synthetic basket data sets. The characteristics that could be used for this
purpose include the frequent itemsets and association rules. The problem of
generating synthetic basket data sets from frequent itemsets is generally
referred to as inverse frequent itemset mining. In this paper, we show that the
problem of approximate inverse frequent itemset mining is {\bf NP}-complete.
Then we propose and analyze an approximate algorithm for approximate inverse
frequent itemset mining, and discuss privacy issues related to the synthetic
basket data set. In particular, we propose an approximate algorithm to
determine the privacy leakage in a synthetic basket data set.
