Research map / Learning theory and algorithms / Submodular and game algorithms
Monotone submodular maximization
Develop approximation algorithms for maximizing submodular functions under cardinality and other constraints.
116 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Submodular and game algorithms, keyword cluster “submodular maximization · submodular functions · monotone”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
17 papers in 2023–24 and 16 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.4% to 6.6%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Submodular Optimization with Routing Constraints (AAAI 2016 · 150 citations)
- 2017 · Guarantees for Greedy Maximization of Non-submodular Functions with Applications (ICML 2017 · 100 citations)
- 2018 · Greed is Still Good: Maximizing Monotone Submodular+Supermodular (BP) Functions (ICML 2018 · 27 citations)
- 2019 · Submodular Maximization beyond Non-negativity: Guarantees, Fast Algorithms, and Applications (ICML 2019 · 62 citations)
- 2020 · Optimization of Chance-Constrained Submodular Functions (AAAI 2020 · 41 citations)
- 2021 · Regularized Submodular Maximization at Scale (ICML 2021 · 15 citations)
- 2022 · Sparsification of Decomposable Submodular Functions (AAAI 2022 · 5 citations)
- 2023 · Submodular Order Functions and Assortment Optimization (ICML 2023 · 7 citations)
- 2024 · Non-monotone Sequential Submodular Maximization (AAAI 2024 · 4 citations)
- 2025 · Corporate Needs You to Find the Difference: Revisiting Submodular and Supermodular Ratio Optimization Problems (NeurIPS 2025 · 1 citation)
- 2026 · A General Framework for Dynamic Consistent Submodular Maximization (ICML 2026 · 0 citations)
Earliest papers here
- Submodular Optimization with Routing Constraints (AAAI 2016 · 150 citations)
- The Power of Optimization from Samples (NeurIPS 2016 · 28 citations)
- Algorithms for Optimizing the Ratio of Submodular Functions (ICML 2016 · 19 citations)
What has been tried
98 papers here report 618 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 11%, hurt 16%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| increase the number of outer-loop repetitions | max-k-cover, Erdős-Rényi graphs · objective value | Helped | An Asymptotically Optimal Approximation Algorithm for Multiobjective Submodular Maximization at Scale (ICML 2025 · 0 citations) | |
| Initialize DCA-LS with the box LASSO solution instead of zero | Integer compressed sensing, m/n approximately 0.25–0.4 · support error | Mixed | Discrete and Continuous Difference of Submodular Minimization (ICML 2025) |
What reviewers will expect
Datasets and baselines named in the 12 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- FISTA · 2 of 12 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 33 papers; from OpenAlex and the papers' affiliations).
- Eindhoven University of Technology · 4 papers
- University of Maryland, College Park · 4 papers
- Google · 4 papers
- Texas A&M University - College Station · 3 papers
- Nanjing University · 2 papers
- East China Normal University · 2 papers
- Zhejiang University · 2 papers
- Soochow University · 2 papers
- University of Science and Technology of China · 2 papers
- Hong Kong University of Science and Technology · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Streaming submodular algorithms (73 papers)
- Submodular influence maximization (33 papers)
Elsewhere in the topic
- Fair division of indivisible goods (130 papers)
- Committee voting rules (120 papers)
- Matching markets and welfare (119 papers)
- Opponent modeling and subgame solving (116 papers)
- Zero-sum game learning dynamics (107 papers)
- Learned auction design (105 papers)
- Correlated equilibria in sequential games (86 papers)
- Equilibrium solvers for adversarial games (25 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).