research-article

Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme

Authors:

Daogao LiuAuthors Info & Claims

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

Pages 789 - 802

https://doi.org/10.1145/3564246.3585229

Published: 02 June 2023 Publication History

Abstract

Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In various scenarios, the searching agent may select an option without making a costly inspection. The variant of the Pandora box problem with non-obligatory inspection has attracted interest from both economics and algorithms researchers. Various simple algorithms have proved suboptimal, with the best known 0.8-approximation algorithm due to Guha et al. (2008). No hardness result for the problem was known.

In this work, we show that it is NP-hard to compute an optimal policy for Pandora’s problem with nonobligatory inspection. We also give a polynomial-time approximation scheme (PTAS) that computes policies with an expected payoff at least (1 − є)-fraction of the optimal, for arbitrarily small є > 0. On the side, we show the decision version of the problem to be in NP.

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Cited By

Berger BEzra TFeldman MFusco F(2024)Pandora’s Problem with Combinatorial CostMathematics of Operations Research10.1287/moor.2023.0248Online publication date: 18-Dec-2024
https://doi.org/10.1287/moor.2023.0248
Beyhaghi HCai L(2023)Recent Developments in Pandora's Box Problem: Variants and ApplicationsACM SIGecom Exchanges10.1145/3699814.369981721:1(20-34)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1145/3699814.3699817
Beyhaghi HCai LSaha BServedio R(2023)Pandora’s Problem with Nonobligatory Inspection: Optimal Structure and a PTASProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585217(803-816)Online publication date: 2-Jun-2023
https://doi.org/10.1145/3564246.3585217

Index Terms

Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms
    1. Online algorithms

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cover image ACM Conferences

STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of Computing

June 2023

1926 pages

ISBN:9781450399135

DOI:10.1145/3564246

General Chair:
Barna Saha
University of California at San Diego, USA
,
Program Chair:
Rocco A. Servedio
Columbia University, USA

Copyright © 2023 ACM.

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Published: 02 June 2023

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Simons award It from Qubit

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STOC '23

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STOC '23: 55th Annual ACM Symposium on Theory of Computing

June 20 - 23, 2023

FL, Orlando, USA

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Cited By

Berger BEzra TFeldman MFusco F(2024)Pandora’s Problem with Combinatorial CostMathematics of Operations Research10.1287/moor.2023.0248Online publication date: 18-Dec-2024
https://doi.org/10.1287/moor.2023.0248
Beyhaghi HCai L(2023)Recent Developments in Pandora's Box Problem: Variants and ApplicationsACM SIGecom Exchanges10.1145/3699814.369981721:1(20-34)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1145/3699814.3699817
Beyhaghi HCai LSaha BServedio R(2023)Pandora’s Problem with Nonobligatory Inspection: Optimal Structure and a PTASProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585217(803-816)Online publication date: 2-Jun-2023
https://doi.org/10.1145/3564246.3585217

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