Average time complexity of decision trees 9783642226601, 3642226604, 9783642270161, 3642270166

Table of contents :
Cover......Page 1
Upper Bound on Average Depth......Page 4
Polynomiality Criterion for Algorithm A......Page 5
Procedure of Optimization......Page 6
Bounds on Average Weighted Depth......Page 7
Greedy Algorithms......Page 9
Algorithms for Decision Tree Construction......Page 11
Introduction......Page 12
Front Matter......Page 2
Theorem of Decomposition......Page 13
Restricted Information Systems......Page 23
Representation of Set of Irredundant Decision Trees......Page 3
Bounds on Average Weighted Depth......Page 18
Corner Point Detection Problem......Page 14
Decision Trees......Page 16
Problems Over Information Systems......Page 15
Complexity Measures of Decision Trees......Page 17
Representing Boolean Functions by Decision Trees......Page 20
Algorithms for Decision Tree Construction......Page 22
Bounds on Average Time Complexity of Decision Trees......Page 26
Known Bounds......Page 27
Upper Bound on Average Depth......Page 29
Process of Building Decision Trees YU,......Page 30
Proofs of Theorems 2.3 and 2.4......Page 31
Proper Problem Decomposition......Page 37
Theorem of Decomposition......Page 38
Example of Decomposable Problem......Page 48
Representing Boolean Functions by Decision Trees......Page 51
Auxiliary Notions......Page 52
Bounds on Function HB(n)......Page 53
Proofs of Propositions 3.1-3.13......Page 55
On Branching Programs with Minimum Average Depth......Page 68
Algorithms for Decision Tree Construction......Page 71
Algorithm A for Decision Tree Construction......Page 72
Representation of Set of Irredundant Decision Trees......Page 73
Procedure of Optimization......Page 76
Greedy Algorithms......Page 79
Modeling Monotonic Boolean Functions by Decision Trees......Page 82
Corner Point Detection Problem......Page 84
Experimental Results......Page 86
On Bounds on Average Depth of Decision Trees Depending Only on Entropy......Page 89
Polynomiality Criterion for Algorithm A......Page 93
Back Matter......Page 95

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