On the complexity of two frequent set generation algorithms

Frequent set generation is normally the first step toward association rule generation, and is usually considered the bottleneck step. Accordingly, many algorithms to generate frequent sets have been proposed. Evaluation of these algorithms is normally done empirically: their running times have been compared on a few or a substantial number of data files. Evaluation of the computational complexity of these algorithms has not much been pursued except to note that every algorithm requires exponential time, because the output size can be exponential in terms qf´ the input size. We develop an alternate method qf´ evaluating algorithms for frequent set generation: we propose evaluating the algorithms according to their computational complexity on several abstractly defined infinite families qf´ data files. We perform this evaluation for Apriori and F P-growth on two infinite families qf´data files, and show that on both families, a variant of F P-growth is unboundedly faster than Apriori as the data file size increases.