# Submodular Secretary Problem with Shortlists

@article{Agrawal2018SubmodularSP,
title={Submodular Secretary Problem with Shortlists},
journal={ArXiv},
year={2018},
volume={abs/1809.05082}
}
• Published 13 September 2018
• Computer Science
• ArXiv
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…

## Tables from this paper

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 $O(k)$.
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 $\frac{1}{p+1}$.
• Computer Science, Mathematics
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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.
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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.
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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.
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• Computer Science
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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
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## References

SHOWING 1-10 OF 35 REFERENCES

• Computer Science, Mathematics
APPROX-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.
• Computer Science
ArXiv
• 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.
• Mathematics, Computer Science
TALG
• 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.
• Mathematics, Computer Science
WINE
• 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.
• Computer Science, Mathematics
Proceedings 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.
• Mathematics, Computer Science
Math. 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.
• Computer Science, Mathematics
2015 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.
• Economics, Education
EC '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.
• Computer Science
IPCO
• 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 .
• Computer Science
SODA
• 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.