# Submodular Secretary Problem with Shortlists

@article{Agrawal2019SubmodularSP, title={Submodular Secretary Problem with Shortlists}, author={Shipra Agrawal and Mohammad Shadravan and Clifford Stein}, journal={ArXiv}, year={2019}, volume={abs/1809.05082} }

In submodular $k$-secretary problem, the goal is to select $k$ items in a randomly ordered input so as to maximize the expected value of a given monotone submodular function on the set of selected items. In this paper, we introduce a relaxation of this problem, which we refer to as submodular $k$-secretary problem with shortlists. In the proposed problem setting, the algorithm is allowed to choose more than $k$ items as part of a shortlist. Then, after seeing the entire input, the algorithm can…

## 17 Citations

### Submodular Matroid Secretary Problem with Shortlists

- Computer Science, MathematicsArXiv
- 2020

An algorithm is designed that achieves a $\frac{1}{2}(1-1/e^2-\epsilon-O(1/k)))$ competitive ratio for any constant $\epsil on>0$, using a shortlist of size $O(k)$.

### Improved Submodular Secretary Problem with Shortlists

- Computer Science, MathematicsArXiv
- 2020

A near optimal approximation algorithm for random-order streaming of monotone submodular functions under cardinality constraints, using memory $O(k poly(1/\epsilon), which exponentially improves the running time and memory of \cite{us} in terms of $1/Â£1 and asymptotically approaches the best known offline guarantee $\frac{1}{p+1}$.

### Streaming Submodular Maximization Under Matroid Constraints

- Computer Science, MathematicsICALP
- 2022

This paper's multi-pass streaming algorithm is tight in that any algorithm with a better guarantee than 1 / 2 must make several passes through the stream and any algorithm that beats the authors' guarantee of 1 − 1 /e must make linearly many passes (as well as an exponential number of value oracle queries).

### Nearly Linear Time Algorithms and Lower Bound for Submodular Maximization

- Computer Science
- 2018

A linear query complexity algorithm is presented that achieves the approximation ratio of $(1-1/e-\varepsilon)$ for cardinality constraint and monotone objective, which is the first deterministic algorithm to achieve the almost optimal approximation using linear number of function evaluations.

### Submodular Streaming in All its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity

- Computer ScienceICML
- 2019

This paper proposes Sieve-Streaming++, which requires just one pass over the data, keeps only $O(k)$ elements and achieves the tight $(1/2)$-approximation guarantee, and demonstrates the efficiency of the algorithms on real-world data summarization tasks for multi-source streams of tweets and of YouTube videos.

### "Bring Your Own Greedy"+Max: Near-Optimal 1/2-Approximations for Submodular Knapsack

- Computer ScienceAISTATS
- 2020

A new rigorous algorithmic framework for a standard formulation of this problem as a submodular maximization subject to a linear (knapsack) constraint is proposed, based on augmenting all partial Greedy solutions with the best additional item.

### Adversarially Robust Submodular Maximization under Knapsack Constraints

- Computer ScienceKDD
- 2019

Experimental results show that the first adversarially robust algorithm for monotone submodular maximization under single and multiple knapsack constraints with scalable implementations in distributed and streaming settings shows strong performance even compared to offline algorithms that are given the set of removals in advance.

### Tight Trade-offs for the Maximum k-Coverage Problem in the General Streaming Model

- Computer SciencePODS
- 2019

A single-pass algorithm is designed that reports an α-approximate solution in $\tildeO (m/α^2 + k)$ space and heavily exploits data stream sketching techniques, which could lead to further connections between vector sketching methods and streaming algorithms for combinatorial optimization tasks.

### Maximum Coverage in the Data Stream Model: Parameterized and Generalized

- Computer ScienceICDT
- 2021

The goal is to design single-pass algorithms that use space that is sublinear in the input size of the data stream model and obtain an algorithm for the parameterized version of the streaming SetCover problem.

### Cardinality constrained submodular maximization for random streams

- Computer ScienceNeurIPS
- 2021

This work simplifies both the algorithm and the analysis, obtaining an exponential improvement in the ε -dependence, and gives a simple (1 /e − ε ) -approximation for non-monotone functions in O ( k/ε ) memory.

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