Average Time Complexity of Decision Trees

ISBN-13: 9783642270161 / Angielski / Miękka / 2013 / 104 str.

Igor Chikalov

Opis

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.

Recenzje

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)

Spis treści

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.