Average Time Complexity of Decision Trees

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.