Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables

In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct e...

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Published in:Procedia computer science Vol. 22; pp. 359 - 365
Main Authors: Chikalov, Igor, Hussain, Shahid, Moshkov, Mikhail
Format: Journal Article
Language:English
Published: Elsevier B.V 2013
Subjects:
monotone Boolean functions
number of nodes and depth of decision trees
Totally optimal decision trees
number of nodes and depth of decision trees
monotone Boolean functions
Totally optimal decision trees
ISSN:1877-0509, 1877-0509
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Abstract In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.
AbstractList In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.
Author Moshkov, Mikhail
Chikalov, Igor
Hussain, Shahid
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Cites_doi 10.1109/SFCS.1998.743453
10.1215/S0012-7094-40-00655-X
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Keywords number of nodes and depth of decision trees
monotone Boolean functions
Totally optimal decision trees
Language English
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References P. Beame, M.E. Saks, J.S. Thathachar, Time-space tradeoffs for branching programs, in: FOCS, 1998, pp. 254-263.
A. Alkhalid, I. Chikalov, M. Moshkov, Constructing an optimal decision tree for fast corner point detection, in: RSKT, 2011, pp. 187-194.
I. Chikalov, S. Hussain, M. Moshkov, Relationships for cost and uncertainty of decision trees, in: A. Skowron, Z. Suraj (Eds.), Rough Sets and Intelligent Systems - Professor ZdzisÅaw Pawlak in Memoriam, Vol. 43 of Intelligent Systems Reference Library, Springer Berlin Heidelberg, 2013, pp. 203-222.
R. Church, Numerical analysis of certain free distributive structures, Duke Mathematical Journal (6) (1940) 732-734.
A. Alkhalid, T. Amin, I. Chikalov, S. Hussain, M. Moshkov, B. Zielosko, Computational Informatics, Social Factors and New Information Technologies: Hypermedia Perspectives and Avant-Garde Experiencies in the Era of Communicability Expansion, Blue Herons, 2011, Ch. Dagger: a tool for analysis and optimization of decision trees and rules, pp. 29-39.
A. Alkhalid, I. Chikalov, M. Moshkov, On algorithm for building of optimal α-decision trees, in: M. S. Szczuka, M. Kryszkiewicz, S. Ramanna, R. Jensen, Q. Hu (Eds.), RSCTC, Springer, Heidelberg, 2010, pp. 438-445.
A. Alkhalid, I. Chikalov, S. Hussain, M. Moshkov, Extensions of dynamic programming as a new tool for decision tree optimization, in: S. Ramanna, L.C. Jain, R.J. Howlett (Eds.), Emerging Paradigms in Machine Learning, Vol. 13 of Smart Innovation, Systems and Technologies, Springer Berlin Heidelberg, 2013, pp. 11-29.
A. Alkhalid, I. Chikalov, M. Moshkov, A tool for study of optimal decision trees, in: J. Yu, S. Greco, P. Lingras, G. Wang, A. Skowron (Eds.), RSKT, Vol. LNCS 6401, Springer, 2010, pp. 353-360.
A. Frank, A. Asuncion, UCI Machine Learning Repository (2010). URL http://archive.ics.uci.edu/ml.
M. J. Moshkov, Time complexity of decision trees, in: J. F. Peters, A. Skowron (Eds.), T. Rough Sets, Vol. 3400 of Lecture Notes in Computer Science, Springer, Heidelberg, 2005, pp. 244-459.
10.1016/j.procs.2013.09.113_bib0040
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References_xml – reference: M. J. Moshkov, Time complexity of decision trees, in: J. F. Peters, A. Skowron (Eds.), T. Rough Sets, Vol. 3400 of Lecture Notes in Computer Science, Springer, Heidelberg, 2005, pp. 244-459.
– reference: A. Alkhalid, I. Chikalov, M. Moshkov, On algorithm for building of optimal α-decision trees, in: M. S. Szczuka, M. Kryszkiewicz, S. Ramanna, R. Jensen, Q. Hu (Eds.), RSCTC, Springer, Heidelberg, 2010, pp. 438-445.
– reference: A. Frank, A. Asuncion, UCI Machine Learning Repository (2010). URL http://archive.ics.uci.edu/ml.
– reference: A. Alkhalid, I. Chikalov, M. Moshkov, Constructing an optimal decision tree for fast corner point detection, in: RSKT, 2011, pp. 187-194.
– reference: A. Alkhalid, I. Chikalov, S. Hussain, M. Moshkov, Extensions of dynamic programming as a new tool for decision tree optimization, in: S. Ramanna, L.C. Jain, R.J. Howlett (Eds.), Emerging Paradigms in Machine Learning, Vol. 13 of Smart Innovation, Systems and Technologies, Springer Berlin Heidelberg, 2013, pp. 11-29.
– reference: P. Beame, M.E. Saks, J.S. Thathachar, Time-space tradeoffs for branching programs, in: FOCS, 1998, pp. 254-263.
– reference: R. Church, Numerical analysis of certain free distributive structures, Duke Mathematical Journal (6) (1940) 732-734.
– reference: A. Alkhalid, T. Amin, I. Chikalov, S. Hussain, M. Moshkov, B. Zielosko, Computational Informatics, Social Factors and New Information Technologies: Hypermedia Perspectives and Avant-Garde Experiencies in the Era of Communicability Expansion, Blue Herons, 2011, Ch. Dagger: a tool for analysis and optimization of decision trees and rules, pp. 29-39.
– reference: I. Chikalov, S. Hussain, M. Moshkov, Relationships for cost and uncertainty of decision trees, in: A. Skowron, Z. Suraj (Eds.), Rough Sets and Intelligent Systems - Professor ZdzisÅaw Pawlak in Memoriam, Vol. 43 of Intelligent Systems Reference Library, Springer Berlin Heidelberg, 2013, pp. 203-222.
– reference: A. Alkhalid, I. Chikalov, M. Moshkov, A tool for study of optimal decision trees, in: J. Yu, S. Greco, P. Lingras, G. Wang, A. Skowron (Eds.), RSKT, Vol. LNCS 6401, Springer, 2010, pp. 353-360.
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SubjectTerms monotone Boolean functions
number of nodes and depth of decision trees
Totally optimal decision trees
Title Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables
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