Data mining is very often regarded as an interactive and iterative process. Users interacting with the data mining system specify the class of patterns of their interest by means of data mining queries involving various types of constraints. It is very likely that a user will execute a series of similar queries, before he or she gets satisfying results. Unfortunately, data mining algorithms currently available suffer from long processing times, which is unacceptable in case of interactive mining. One possible solution, applicable in certain cases, is exploiting materialized results of previous queries when answering a new query. In this paper we discuss cost-based data mining query optimization in presence of materialized results of previous queries, focusing on one of the popular data mining techniques, called discovery of sequential patterns. Keywords: data mining, sequential patterns, query optimization