Search Results

Documents authored by Nielsen, Mads Anker

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.26
Non-Adaptive Evaluation of k-of- n Functions: Tight Gap and a Unit-Cost PTAS

Authors: Mads Anker Nielsen, Lars Rohwedder, and Kevin Schewior

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of k-of-n functions: There are independent Boolean random variables x_1,… ,x_n where each variable i has a known probability p_i of taking value 1, and a known cost c_i that can be paid to find out its value. The value of the function is 1 iff there are at least k 1s among the variables. The goal is to efficiently compute a strategy that, at minimum expected cost, tests the variables until the function value is determined. While an elegant polynomial-time exact algorithm is known when tests can be made adaptively, we focus on the non-adaptive variant, for which much less is known. First, we show a clean and tight lower bound of 2 on the adaptivity gap, i.e., the worst-case multiplicative loss in the objective function caused by disallowing adaptivity, of the problem. This improves the tight lower bound of 3/2 for the unit-cost variant. Second, we give a PTAS for computing the best non-adaptive strategy in the unit-cost case, the first PTAS for an SBFE problem. At the core, our scheme establishes a novel notion of two-sided dominance (w.r.t. the optimal solution) by guessing so-called milestone tests for a set of carefully chosen buckets of tests. To turn this technique into a polynomial-time algorithm, we use a decomposition approach paired with a random-shift argument.
Cite as

Mads Anker Nielsen, Lars Rohwedder, and Kevin Schewior. Non-Adaptive Evaluation of k-of- n Functions: Tight Gap and a Unit-Cost PTAS. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{nielsen_et_al:LIPIcs.APPROX/RANDOM.2025.26,
  author =	{Nielsen, Mads Anker and Rohwedder, Lars and Schewior, Kevin},
  title =	{{Non-Adaptive Evaluation of k-of- n Functions: Tight Gap and a Unit-Cost PTAS}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.26},
  URN =		{urn:nbn:de:0030-drops-243920},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.26},
  annote =	{Keywords: Approximation scheme, Boolean functions, stochastic combinatorial optimization, stochastic function evaluation, sequential testing, adaptivity}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact