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AbstractThe study of algorithms for decision tree construction was initiated in 1960s. The first algorithms are based on the separation heuristic [13, 31] that at each step tries dividing the set of objects as evenly as possible. Later Garey and Graham  showed that such algorithm may construct decision trees whose average depth is arbitrarily far from the minimum. Hyafil and Rivest in  proved NP-hardness of DT problem that is constructing a tree with the minimum average depth for a diagnostic problem over 2-valued information system and uniform probability distribution. Cox et al. in  showed that for a two-class problem over information system, even finding the root node attribute for an optimal tree is an NP-hard problem. © Springer-Verlag Berlin Heidelberg 2011.