Time and space complexity of deterministic and nondeterministic decision trees
KAUST DepartmentApplied Mathematics and Computational Science Program
Computational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Computer, Electrical and Mathematical Sciences and Engineering Division and Computational Bioscience Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
Extensions of Dynamic Programming, Machine Learning and Discrete Optimization Research Group
Permanent link to this recordhttp://hdl.handle.net/10754/674930
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AbstractIn this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a problem over information system, which is described by a finite number of attributes and a mapping associating a decision to each tuple of attribute values. As algorithms for problem solving, we use deterministic and nondeterministic decision trees. As time and space complexity, we study the depth and the number of nodes in the decision trees. In the worst case, with the growth of the number of attributes in the problem description, (i) the minimum depth of deterministic decision trees grows either almost as logarithm or linearly, (ii) the minimum depth of nondeterministic decision trees either is bounded from above by a constant or grows linearly, (iii) the minimum number of nodes in deterministic decision trees has either polynomial or exponential growth, and (iv) the minimum number of nodes in nondeterministic decision trees has either polynomial or exponential growth. Based on these results, we divide the set of all infinite binary information systems into five complexity classes, and study for each class issues related to time-space trade-off for decision trees.
CitationMoshkov, M. (2022). Time and space complexity of deterministic and nondeterministic decision trees. Annals of Mathematics and Artificial Intelligence. https://doi.org/10.1007/s10472-022-09814-1
SponsorsResearch reported in this publication was supported by King Abdullah University of Science and Technology (KAUST). The author is greatly indebted to the anonymous reviewers for very useful remarks and suggestions.
PublisherSpringer Science and Business Media LLC
Except where otherwise noted, this item's license is described as Archived with thanks to Annals of Mathematics and Artificial Intelligence under a Creative Commons license, details at: https://creativecommons.org/licenses/by/4.0