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This monograph generalizes several known results on the topic and considers a number of fresh problems. Combinatorics, probability theory and complexity theory are used in the proofs, as well as concepts from discrete mathematics and computer science.

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Decision tree is a widely used form of representing algorithms and knowledge. Compact data models

and fast algorithms require optimization of tree complexity. This book is a research monograph on

average time complexity of decision trees. It generalizes several known results and considers a number of new problems.

The book contains exact and approximate algorithms for decision tree optimization, and bounds on minimum average time

complexity of decision trees. Methods of combinatorics, probability theory and complexity theory are used in the proofs as

well as concepts from various branches of discrete mathematics and computer science. The considered applications include

the study of average depth of decision trees for Boolean functions from closed classes, the comparison of results of the performance

of greedy heuristics for average depth minimization with optimal decision trees constructed by dynamic programming algorithm,

and optimization of decision trees for the corner point recognition problem from computer vision.

The book can be interesting for researchers working on time complexity of algorithms and specialists
in test theory, rough set theory, logical analysis of data and machine learning.

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1 Introduction.- 2 Bounds on Average Time Complexity of Decision Trees.- 3 Representing Boolean Functions by Decision Trees.- 4 Algorithms for Decision Tree Construction.- 5 Problems Over Information Systems.

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From the reviews:

"The book contains several previously known results on the average time complexity of decision trees for a number of new problems. The author presents bounds on the minimum average time complexity of decision trees. ... In summary, the results presented in the book may be of interest for researchers in test theory, rough set theory, and logical analysis of data and machine learning. The book is suitable for a graduate or PhD course." (Jerzy Martyna, Zentralblatt MATH, Vol. 1244, 2012)

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