Online submodular maximization: beating 1/2 made simple

@article{Buchbinder2018OnlineSM,
  title={Online submodular maximization: beating 1/2 made simple},
  author={Niv Buchbinder and Moran Feldman and Mohit Garg},
  journal={Mathematical Programming},
  year={2018},
  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… 
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17 Citations
Background Citations
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Methods Citations
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17 Citations

Online submodular maximization: beating 1/2 made simple

An upper bound of 0.574 is proved on the competitive ratio of the greedy algorithm, ruling out the possibility that the competitiveness of this natural algorithm matches the optimal offline approximation ratio of 1-1/e.

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

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.

The Power of Subsampling in Submodular Maximization

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An Optimal Streaming Algorithm for Submodular Maximization with a Cardinality Constraint

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Edge-Weighted Online Bipartite Matching

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

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 $O(k \log k)$.

Sublinear Time Algorithm for Online Weighted Bipartite Matching

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

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

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.

D S ] 1 5 Ju l 2 01 8 Deterministic ( 1 / 2 + ε )-Approximation for Submodular Maximization over a Matroid Niv Buchbinder

This algorithm is the first deterministic algorithm known to improve over the 1/2approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsely and Fisher in 1978.

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