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Approximation Algorithms for Stochastic Submodular Set Cover with Applications to Boolean Function Evaluation and Min-Knapsack

Authors:

Amol Deshpande,

Lisa Hellerstein,

Devorah KletenikAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 12, Issue 3

Article No.: 42, Pages 1 - 28

https://doi.org/10.1145/2876506

Published: 25 April 2016 Publication History

Abstract

We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem.

We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause.

We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.

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Index Terms

Approximation Algorithms for Stochastic Submodular Set Cover with Applications to Boolean Function Evaluation and Min-Knapsack
1. Computing methodologies
  1. Machine learning
    1. Learning paradigms
      1. Supervised learning
        Cost-sensitive learning
  2. Symbolic and algebraic manipulation
    1. Representation of mathematical objects
      1. Representation of Boolean functions
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Packing and covering problems
      2. Stochastic approximation
  2. Theory and algorithms for application domains
    1. Database theory
      1. Database query processing and optimization (theory)

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 12, Issue 3

June 2016

408 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2930058

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2016 ACM.

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Publication History

Published: 25 April 2016

Accepted: 01 January 2016

Revised: 01 January 2016

Received: 01 December 2014

Published in TALG Volume 12, Issue 3

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Ghuge RGupta ANagarajan V(2024)The Power of Adaptivity for Stochastic Submodular CoverOperations Research10.1287/opre.2022.238872:3(1156-1176)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1287/opre.2022.2388
Agarwal AGhuge RNagarajan V(2024)Semi-Bandit Learning for Monotone Stochastic Optimization*2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00083(1260-1274)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00083
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