Upper bound on the length of generalized disjunction-free patterns

A number of lossless representations of frequent patterns were proposed in recent years. The representation that consists of all frequent closed itemsets and the representations based on generalized disjunction-free patterns or on non-derivable itemsets are proven the most concise ones. Experiments show further that the latter ones are by a few orders of magnitude more concise (and determinable) than the former one. As follows from experiments, the representations based on generalized disjunction-free patterns are also more concise than the available in the literature representations of frequent patterns, which determine supports of patterns in an approximate way. In this paper, we provide an upper bound on the length of generalized disjunction-free patterns. The bound determines the maximum number of scans of the database carried out by a priori-like algorithms discovering the representations based on generalized disjunction-free patterns.