# Online submodular maximization: beating 1/2 made simple

@article{Buchbinder2019OnlineSM, title={Online submodular maximization: beating 1/2 made simple}, author={Niv Buchbinder and Moran Feldman and Mohit Garg}, journal={Mathematical Programming}, year={2019}, pages={1-21} }

The Submodular Welfare Maximization problem (SWM) captures an important subclass of combinatorial auctions and has been studied extensively. In particular, it has been studied in a natural online setting in which items arrive one-by-one and should be allocated irrevocably upon arrival. For this setting, Korula et al. (SIAM J Comput 47(3):1056–1086, 2018) were able to show that the greedy algorithm is 0.5052-competitive when the items arrive in a uniformly random order. Unfortunately, however…

## 16 Citations

### Making a Sieve Random: Improved Semi-Streaming Algorithm for Submodular Maximization under a Cardinality Constraint

- Computer ScienceArXiv
- 2019

This work manages to adapt Sieve-Streaming to non-monotone objective functions by introducing a "just right" amount of randomness into it, and gets a semi-streaming polynomial time $4.282$-approximation algorithm for non- monotone objectives.

### Streaming Maximization of Submodular Functions Subject to Cardinality Constraint

- Computer Science
- 2020

This work studies the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model, and presents a single-pass streaming algorithm that uses roughly O(k/ε2) memory and enjoys a fast update time of O( log k+log(1/α) ε2 ) per element.

### The Power of Subsampling in Submodular Maximization

- Computer ScienceMath. Oper. Res.
- 2022

Subsampling is proposed as a unified algorithmic technique for submodular maximization in centralized and online settings and it is shown that this approach leads to optimal/state-of-the-art results despite being much simpler than existing methods.

### An Optimal Streaming Algorithm for Submodular Maximization with a Cardinality Constraint

- Computer ScienceMathematics of Operations Research
- 2022

We study the problem of maximizing a nonmonotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi) streaming algorithm that…

### Edge-Weighted Online Bipartite Matching

- Computer Science2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
- 2020

This paper presents the first online algorithm that breaks the long-standing 1/2 barrier and achieves a competitive ratio of at least 0.5086, and can be seen as strong evidence that edge-weighted bipartite matching is strictly easier than submodular welfare maximization in the online setting.

### Submodular Secretary Problem with Shortlists

- Computer ScienceITCS
- 2019

A polynomial time algorithm is given that substantially improves upon the previously best known approximation factor of $1/2 + 8 \times 10^{-14}$ [Norouzi-Fard et al. 2018] that used a memory buffer of size $O(k \log k)$.

### Online Assortment Optimization for Two-sided Matching Platforms

- Computer ScienceEC
- 2021

This work considers the online assortment optimization problem faced by a two-sided matching platform that hosts a set of suppliers waiting to match with a customer, and develops specialized balancing algorithms, which are preference-aware, that leverage general information about the suppliers' choice models.

### Sublinear Time Algorithm for Online Weighted Bipartite Matching

- Computer ScienceArXiv
- 2022

This work provides the theoretical foundation for computing the weights approximately and shows that, with the proposed randomized data structures, the weights can be computed in sublinear time while still preserving the competitive ratio of the matching algorithm.

### On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching

- Computer Science
- 2022

It is proved that the canonical perturbation function is the unique optimal perturbations function for vertex-weighted online bipartite matching, and the online budget-additive welfare maximization problem that is intermediate between AdWords and AdWords with unknown budgets is proposed.

### Robust Algorithms for Online k-means Clustering

- Computer ScienceALT
- 2020

A modified adaptive sampling procedure is given that obtains a better approximation ratio and is shown how to perform adaptive sampling when data has outliers, thus rendering distance-based sampling prone to picking the outliers.

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