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dc.contributor.authorChikalov, Igor
dc.date.accessioned2015-08-03T09:02:01Z
dc.date.available2015-08-03T09:02:01Z
dc.date.issued2011
dc.identifier.citationChikalov, I. (2011). Bounds on Average Time Complexity of Decision Trees. Average Time Complexity of Decision Trees, 15–39. doi:10.1007/978-3-642-22661-8_2
dc.identifier.isbn9783642226601
dc.identifier.issn18684394
dc.identifier.doi10.1007/978-3-642-22661-8_2
dc.identifier.urihttp://hdl.handle.net/10754/561674
dc.description.abstractIn this chapter, bounds on the average depth and the average weighted depth of decision trees are considered. Similar problems are studied in search theory [1], coding theory [77], design and analysis of algorithms (e.g., sorting) [38]. For any diagnostic problem, the minimum average depth of decision tree is bounded from below by the entropy of probability distribution (with a multiplier 1/log2 k for a problem over a k-valued information system). Among diagnostic problems, the problems with a complete set of attributes have the lowest minimum average depth of decision trees (e.g, the problem of building optimal prefix code [1] and a blood test study in assumption that exactly one patient is ill [23]). For such problems, the minimum average depth of decision tree exceeds the lower bound by at most one. The minimum average depth reaches the maximum on the problems in which each attribute is "indispensable" [44] (e.g., a diagnostic problem with n attributes and kn pairwise different rows in the decision table and the problem of implementing the modulo 2 summation function). These problems have the minimum average depth of decision tree equal to the number of attributes in the problem description. © Springer-Verlag Berlin Heidelberg 2011.
dc.publisherSpringer Nature
dc.titleBounds on Average Time Complexity of Decision Trees
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalAverage Time Complexity of Decision Trees
kaust.personChikalov, Igor


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