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Improved Deterministic Algorithms for Non-monotone Submodular Maximization
Data Structures and Algorithms · Submitted 30 Aug 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization.
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The abstract, sentence by sentence
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic $0.283-o(1)$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/4$ approximation ratio. For the knapsack constraint, we provide a deterministic $1/4$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/6$ approximation ratio. For the linear packing constraints with large widths, we provide a deterministic $1/6-\epsilon$ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Submodular maximization is one of the central topics in combinatorial optimization. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | It has found numerous applications in the real world. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s2 | In the past decades, a series of algorithms have been proposed for this problem. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s3 | However, most of the state-of-the-art algorithms are randomized. | background 0.56 | 0.06 | 0.02 | asserted 1.00 |
| s4 | There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. | gap 1.00 | 0.08 | 0.04 | asserted 1.00 |
| s5 | In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. | contribution 1.00 | 0.95 | 0.82 | asserted 1.00 |
| s6 | Specifically, for the matroid constraint, we provide a deterministic $0.283-o(1)$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/4$ approximation ratio. | result 0.74 | 0.96 | 0.21 | asserted 1.00 |
| s7 | For the knapsack constraint, we provide a deterministic $1/4$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/6$ approximation ratio. | result 0.70 | 0.94 | 0.13 | asserted 1.00 |
| s8 | For the linear packing constraints with large widths, we provide a deterministic $1/6-\epsilon$ approximation algorithm. | result 0.61 | 0.95 | 0.10 | asserted 1.00 |
| s9 | To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints. | gap 0.86 | 0.23 | 0.06 | asserted 0.88 |
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Original abstract
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic $0.283-o(1)$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/4$ approximation ratio. For the knapsack constraint, we provide a deterministic $1/4$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/6$ approximation ratio. For the linear packing constraints with large widths, we provide a deterministic $1/6-\epsilon$ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints.
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2 arXiv papers cite this in 3 sentences
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It must be noted that our method differs from the Twin Greedy-based algorithms [ref] , which update both candidate sets at the same iterations but do not allow the integration of the threshold sampling algorithm for parallelization.
Improved Parallel Algorithm for Non-Monotone Submodular Maximization under Knapsack Constraint · Introduction · 0.97
Cites it as background 1 paper
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Later, several works concentrated on improving both approximation factor and query complexity [ref] .
Improved Parallel Algorithm for Non-Monotone Submodular Maximization under Knapsack Constraint · Related Works · 0.92
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