Decision Trees for Function Evaluation: Simultaneous Optimization of Worst and Expected Cost

In several applications of automatic diagnosis and active learning, a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. In general, the process of reading the value of a vari...

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Bibliographic Details
Published in:Algorithmica 2017-11, Vol.79 (3), p.763-796
Main Authors: Cicalese, Ferdinando, Laber, Eduardo, Saettler, Aline
Format: Article
Language:English
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Decision trees
Mathematical analysis
Mathematics of Computing
Theory of Computation
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Summary:In several applications of automatic diagnosis and active learning, a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. In general, the process of reading the value of a variable might involve some cost. This cost should be taken into account when deciding the next variable to read. The goal is to design a strategy for evaluating the function incurring little cost (in the worst case or in expectation according to a prior distribution on the possible variables’ assignments). Our algorithm builds a strategy (decision tree) which attains a logarithmic approximation simultaneously for the expected and worst cost spent. This is best possible under the assumption that P ≠ NP .
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-016-0225-9