research-article

Deterministic Algorithms for Submodular Maximization Problems

Authors:

Niv Buchbinder,

Moran FeldmanAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 3

Article No.: 32, Pages 1 - 20

https://doi.org/10.1145/3184990

Published: 16 June 2018 Publication History

Abstract

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area, most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algorithms. Derandomization of algorithms for general submodular function maximization seems hard since the access to the function is done via a value oracle. This makes it hard, for example, to apply standard derandomization techniques such as conditional expectations. Therefore, an interesting fundamental problem in this area is whether randomization is inherently necessary for obtaining good approximation ratios.

In this work, we give evidence that randomization is not necessary for obtaining good algorithms by presenting a new technique for derandomization of algorithms for submodular function maximization. Our high level idea is to maintain explicitly a (small) distribution over the states of the algorithm, and carefully update it using marginal values obtained from an extreme point solution of a suitable linear formulation. We demonstrate our technique on two recent algorithms for unconstrained submodular maximization and for maximizing a submodular function subject to a cardinality constraint. In particular, for unconstrained submodular maximization we obtain an optimal deterministic 1/2-approximation showing that randomization is unnecessary for obtaining optimal results for this setting.

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Chen YKuhnle ASingh ASun YAkoglu LGunopulos DYan XKumar ROzcan FYe J(2023)Approximation Algorithms for Size-Constrained Non-Monotone Submodular Maximization in Deterministic Linear TimeProceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3580305.3599259(250-261)Online publication date: 6-Aug-2023
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Index Terms

Deterministic Algorithms for Submodular Maximization Problems
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 3

Special Issue on SODA’16 and Regular Papers

July 2018

393 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3233176

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2018 ACM.

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Association for Computing Machinery

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Publication History

Published: 16 June 2018

Accepted: 01 January 2018

Received: 01 March 2016

Published in TALG Volume 14, Issue 3

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Niazadeh RGolrezaei NWang JSusan FBadanidiyuru A(2023)Online Learning via Offline Greedy AlgorithmsManagement Science10.1287/mnsc.2022.455869:7(3797-3817)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1287/mnsc.2022.4558
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https://dl.acm.org/doi/10.1145/3580305.3599259
Buchbinder NFeldman MGarg M(2023)Deterministic \(\boldsymbol{(\unicode{x00BD}+\varepsilon)}\) -Approximation for Submodular Maximization over a MatroidSIAM Journal on Computing10.1137/19M125515X52:4(945-967)Online publication date: 27-Jul-2023
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