Query Minimization under Stochastic Uncertainty
Abstract
We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that, for the sorting problem, such a decision tree can be found in polynomial time. For the problem of finding the data item with minimum value, we have some evidence for hardness. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.
Cite
@article{arxiv.2010.03517,
title = {Query Minimization under Stochastic Uncertainty},
author = {Steven Chaplick and Magnús M. Halldórsson and Murilo S. de Lima and Tigran Tonoyan},
journal= {arXiv preprint arXiv:2010.03517},
year = {2021}
}
Comments
To be published in Theoretical Computer Science. Since the previous version, the time consumption of the sorting algorithm was improved to $\mathrm{O}(n^5)$. Partially supported by Icelandic Research Fund grant 174484-051 and by EPSRC grant EP/S033483/1. A preliminary version of this paper appeared in volume 12118 of LNCS (LATIN 2020), pp. 181--193, 2020. DOI: 10.1007/978-3-030-61792-9_15