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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