# Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models

arXiv: https://arxiv.org/abs/2206.09563 · HTML: https://mlsanity.com/paper/2206.09563/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [One Million Scenes for Autonomous Driving: ONCE Dataset](https://mlsanity.com/paper/2106.11037/) (2021)
- [Lazier Than Lazy Greedy](https://mlsanity.com/paper/1409.7938/) (2014)
- [Randomized Composable Core-sets for Distributed Submodular Maximization](https://mlsanity.com/paper/1506.06715/) (2015)
- [S3VAADA: Submodular Subset Selection for Virtual Adversarial Active Domain Adaptation](https://mlsanity.com/paper/2109.08901/) (2021)
- [Regularized Submodular Maximization at Scale](https://mlsanity.com/paper/2002.03503/) (2020)
- [Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly](https://mlsanity.com/paper/1706.03583/) (2017)
- [Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity](https://mlsanity.com/paper/1807.07889/) (2018)
- [Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity](https://mlsanity.com/paper/1808.06932/) (2018)
- [Submodular Streaming in All its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity](https://mlsanity.com/paper/1905.00948/) (2019)
- [The Power of Randomization: Distributed Submodular Maximization on Massive Datasets](https://mlsanity.com/paper/1502.02606/) (2015)
- [An Exponential Speedup in Parallel Running Time for Submodular Maximization without Loss in Approximation](https://mlsanity.com/paper/1804.06355/) (2018)
- [The FAST Algorithm for Submodular Maximization](https://mlsanity.com/paper/1907.06173/) (2019)
- [Submodular Maximization with Nearly-optimal Approximation and Adaptivity in Nearly-linear Time](https://mlsanity.com/paper/1804.05379/) (2018)
- [A New Framework for Distributed Submodular Maximization](https://mlsanity.com/paper/1507.03719/) (2015)
- [Parallel Algorithm for Non-Monotone DR-Submodular Maximization](https://mlsanity.com/paper/1905.13272/) (2019)
- [Submodular Function Maximization in Parallel via the Multilinear Relaxation](https://mlsanity.com/paper/1807.08678/) (2018)
- [Submodular Optimization in the MapReduce Model](https://mlsanity.com/paper/1810.01489/) (2018)
- [Comparing Apples and Oranges: Query Tradeoff in Submodular Maximization](https://mlsanity.com/paper/1410.0773/) (2014)
- [Submodular Batch Selection for Training Deep Neural Networks](https://mlsanity.com/paper/1906.08771/) (2019)
- [Quick Streaming Algorithms for Maximization of Monotone Submodular Functions in Linear Time](https://mlsanity.com/paper/2009.04979/) (2020)
- [Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint](https://mlsanity.com/paper/2009.01947/) (2020)
- [Best of Both Worlds: Practical and Theoretically Optimal Submodular Maximization in Parallel](https://mlsanity.com/paper/2111.07917/) (2021)
- [Submodular Optimization Problems and Greedy Strategies: A Survey](https://mlsanity.com/paper/1905.03308/) (2019)

## Built on by (most cited first, 1 of 1)

- [Accelerated Relax-and-Round for Concave Coverage Problems](https://mlsanity.com/paper/2605.06900/) (2026)

## Abstract (arXiv)

Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long as the centralized algorithm satisfies a certain consistency property -- which had previously only been known to be satisfied by the standard greedy and continous greedy algorithms. A separate line of work has studied parallelizability of submodular maximization in the adaptive complexity model, where each thread may have access to the entire ground set. For the size-constrained maximization of a monotone and submodular function, we show that several sublinearly adaptive (highly parallelizable) algorithms satisfy the consistency property required to work in the MR setting, which yields practical, parallelizable and distributed algorithms. Separately, we develop the first distributed algorithm with linear query complexity for this problem. Finally, we provide a method to increase the maximum cardinality constraint for MR algorithms at the cost of additional MR rounds.