# Submodular Secretary Problem with Shortlists

@article{Agrawal2018SubmodularSP, title={Submodular Secretary Problem with Shortlists}, author={Shipra Agrawal and Mohammad Shadravan and Clifford Stein}, journal={ArXiv}, year={2018}, 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…

## 18 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.

### 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.

### The one-way communication complexity of submodular maximization with applications to streaming and robustness

- Computer ScienceSTOC
- 2020

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various…

### Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation

- Computer Science, MathematicsICALP
- 2022

This work gives an offline fixed-parameter tractable algorithm that guarantees a 0 .

## References

SHOWING 1-10 OF 35 REFERENCES

### Submodular Secretary Problems: Cardinality, Matching, and Linear Constraints

- Computer Science, MathematicsAPPROX-RANDOM
- 2017

This work studies various generalizations of the secretary problem with submodular objective functions and improves over previously best known competitive ratios, using a generalization of the algorithm for the classic secretary problem.

### The submodular secretary problem under a cardinality constraint and with limited resources

- Computer ScienceArXiv
- 2017

This work proposes a $0.1933$-competitive anytime algorithm, which performs only a single evaluation of the marginal contribution for each observed item, and requires a memory of order only $k$ (up to logarithmic factors), where k is the cardinality constraint.

### Submodular secretary problem and extensions

- Mathematics, Computer ScienceTALG
- 2013

This article considers a very general setting of the classic secretary problem, in which the goal is to select k secretaries so as to maximize the expectation of a submodular function which defines efficiency of the selected secretarial group based on their overlapping skills, and presents the first constant-competitive algorithm for this case.

### Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms

- Mathematics, Computer ScienceWINE
- 2010

These ideas are extended to give a simple greedy-based constant factor algorithms for non-monotone submodular maximization subject to a knapsack constraint, and for (online) secretary setting subject to uniform matroid or a partition matroid constraint.

### Improved algorithms and analysis for secretary problems and generalizations

- Computer Science, MathematicsProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

The methods are very intuitive and apply to some generalizations of the classical secretary problem, and derive a lower bound on the trade-off between the probability of selecting the best object and its expected rank.

### Submodular maximization meets streaming: matchings, matroids, and more

- Mathematics, Computer ScienceMath. Program.
- 2015

A general pattern for algorithms that maximize linear weight functions over “independent sets” is identified and it is proved that such algorithms can be adapted to maximize a submodular function.

### The Submodular Secretary Problem Goes Linear

- Computer Science, Mathematics2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

It is shown that any O(1)-competitive algorithm for MSP, even restricted to a particular matroid class, can be transformed in a black-box way to an O( 1)- competitive algorithm for SMSP over the same matroidclass, which implies that SMSP is not harder than MSP.

### The adwords problem: online keyword matching with budgeted bidders under random permutations

- Economics, EducationEC '09
- 2009

The problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit, is considered, and the current literature on this problem is extended by considering the setting where the keywords arrive in a random order.

### Online submodular maximization: beating 1/2 made simple

- Computer ScienceIPCO
- 2019

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 $$1-1/e$$ 1 - 1 / e .

### Submodular Maximization with Cardinality Constraints

- Computer ScienceSODA
- 2014

Improved approximations for two variants of the cardinality constraint for non-monotone functions are presented and a simple randomized greedy approach is presented where in each step a random element is chosen from a set of "reasonably good" elements.