Efficient SQL-querying method for data mining in large data bases

Data mining can be understood as a process of extraction of knowledge hidden in very large data sets. Often data mining techniques (e.g. discretization or decision tree) are based on searching for an optimal partition of data with respect to some optimization criterion. In this paper, we investigate the problem of optimal binary partition of continuous attribute domain for large data sets stored in relational data bases (RDB). The critical for time complexity of algorithms solving this problem is the number of simple SQL queries like SELECT COUNT FROM... WHERE attribute BETWEEN (related to some interval of attribute values) necessary to construct such partitions. We assume that the answer time for such queries does not depend on the interval length. Using straightforward approach to optimal partition selection (with respect to a given measure), the number of necessary queries is of order O(N), where N is the number of preassumed partitions of the searching space. We show some properties of considered optimization measures, that allow to reduce the size of searching space. Moreover, we prove that using only O(log N) simple queries, one can construct the partition very close to optimal.