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

作者：Cicalese Ferdinando; Laber Eduardo^*; Saettler Aline

来源：Algorithmica, 2017, 79(3): 763-796.

DOI：10.1007/s00453-016-0225-9

• Decision tress
• Approximation algorithms
• Hardness of approximation
• Function evaluation

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 not equal NP.

• 出版日期2017-11