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Igor Chikalov's Average Time Complexity of Decision Trees PDF

By Igor Chikalov

Decision tree is a universal type of representing algorithms and information. Compact information types

and quick algorithms require optimization of tree complexity. This booklet is a learn monograph on

average time complexity of determination timber. It generalizes a number of recognized effects and considers a few new difficulties.

The publication comprises unique and approximate algorithms for selection tree optimization, and boundaries on minimal general time

complexity of determination bushes. equipment of combinatorics, likelihood concept and complexity idea are utilized in the proofs as

well as suggestions from numerous branches of discrete arithmetic and laptop technology. The thought of functions include

the research of commonplace intensity of determination timber for Boolean services from closed sessions, the comparability of result of the functionality

of grasping heuristics for commonplace intensity minimization with optimum determination bushes developed by way of dynamic programming algorithm,

and optimization of determination timber for the nook element popularity challenge from laptop vision.

The booklet may be fascinating for researchers engaged on time complexity of algorithms and experts

in try out conception, tough set thought, logical research of knowledge and desktop learning.

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T ) in which the values of the attributes corresponding to C2 and all circles that contains C2 are set to 1, and all other elements are set to 0. Let us show n ¯ , δ) ≥ m + 1. Denote fi0 the attribute corresponding to C2 , and that M (zm fi1 , . . , fim the attributes corresponding to the first order circles enclosed into C2 . Let S = {fj1 (x) = δj1 , . . , fjk (x) = δjk } be an arbitrary system of n (x) ≡ const equations that either does not have a solution on the A or zm on the set of solutions.

From the definition of the ¯ tree Φ it follows that the terminal node of the path ξ δ belongs to the subtree Γ˜i . Since the decision tree Γi solves the problem zi , the terminal node of the path ξi is assigned with the number νi (δ1i , . . , δni i ). From the definition of ¯ = νi (δ i , . . , δ i ). Therefore, Φ solves the proper decomposition we have ν(δ) 1 ni problem z. Let us show that Φ is optimal for z and P . 5 it follows that there exists a decision tree G for the problem z that solves z, is optimal for z and P , and is completely ordered.

1 ([48]). Let B be a closed class of Boolean functions and n be a natural number. Then a) if B ∈ {O2 , O3 , O7 }, then GB (n) = 0; b) if B ∈ {O1 , O4 , O5 , O6 , O8 , O9 }, then GB (n) = 1; n, if n is odd , c) if B ∈ {L4 , L5 }, then GB (n) = n − 1 , if n is even ; d) if B ∈ {D1 , D2 , D3 }, then GB (n) = n, if n ≥ 3 , 1 , if n ≤ 2 ; e) if the class B does not coincide with any classes mentioned in (a) – (d), then GB (n) = n. 13. These theorems characterize the relation between HB (n) and GB (n) for each closed class of Boolean functions.

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