New results for the k-secretary problem

Albers, Susanne; Ladewig, Leon

doi:10.1016/j.tcs.2021.02.022

Cited by 10 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [11], an algorithm with a competitive ratio of 1/(1 − 5/ √ k), for large enough k, with a matching lower bound of Ω(1/(1−1/ √ k)) is presented. Furthermore, [4] contains an algorithm that is e-competitive for any k. Some progress for the case of small k was made in [3]. The Knapsack Secretary Problem introduced by [4] is equivalent to the Online Knapsack Problem in the random order model.…”

Section: Related Workmentioning

confidence: 99%

Reading Articles Online

Karrenbauer¹,

Kovalevskaya²

2020

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

We study the online problem of reading articles that are listed in an aggregated form in a dynamic stream, e.g., in news feeds, as abbreviated social media posts, or in the daily update of new articles on arXiv. In such a context, the brief information on an article in the listing only hints at its content. We consider readers who want to maximize their information gain within a limited time budget, hence either discarding an article right away based on the hint or accessing it for reading. The reader can decide at any point whether to continue with the current article or skip the remaining part irrevocably. In this regard, Reading Articles Online, RAO, does differ substantially from the Online Knapsack Problem, but also has its similarities. Under mild assumptions, we show that any α-competitive algorithm for the Online Knapsack Problem in the random order model can be used as a black box to obtain an (e + α)C-competitive algorithm for RAO, where C measures the accuracy of the hints with respect to the information profiles of the articles. Specifically, with the current best algorithm for Online Knapsack, which is 6.65 < 2.45e-competitive, we obtain an upper bound of 3.45eC on the competitive ratio of RAO. Furthermore, we study a natural algorithm that decides whether or not to read an article based on a single threshold value, which can serve as a model of human readers. We show that this algorithmic technique is O(C)-competitive. Hence, our algorithms are constant-competitive whenever the accuracy C is a constant.

show abstract

Section: Related Workmentioning

confidence: 99%

Reading Articles Online

Karrenbauer¹,

Kovalevskaya²

2020

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

show abstract

“…Another problem closely related to the random order model is the secretary problem [14,26], that is, a special case of the online knapsack problem in which the weights are uniform and equal to the weight constraint. One natural generalization of the latter is the k-secretary problem [2,11,25], where k elements need to be selected, as well as the matroid secretary problem [6,15], where elements of a weighted matroid arrive in random order, and in both of these, the goal is to maximize the combined value of the selected elements. Other variants of online knapsack presented in the literature include removable models, where removals can incur no cost or a cancellation cost [3,4,17,18,20], reservation costs [7], an expected capacity constraint [32], and resource buffering [19].…”

Section: Related Workmentioning

confidence: 99%

“…In the remainder of this paper, we analyze the performance of A S and A K . The algorithm A S and its analysis are similar to the algorithm A L and its analysis in [1] based on the singleref algorithm [2] for the k-secretary problem. The algorithm A K and its analysis extend the approach of [1] to consider the possibility of packing items fractionally.…”

Section: Application Of the Blended Approach In The Fractional Casementioning

confidence: 99%

“…The following is an adaptation of single-ref developed for the k-secretary problem in [2] and applied to the knapsack setting in [1]. There is a useful connection between the online knapsack problem under random arrival order and the k-secretary problem.…”

Section: Secretary Algorithm a Smentioning

confidence: 99%

“…Items whose size exceeds the capacity of the knapsack can be cut at the knapsack capacity 2. It can be accomplished in polynomial time by fixing a random (but consistent) tie-breaking between elements of the same value, based for instance on the identifier of the element[5].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Improved Online Algorithm for Fractional Knapsack in the Random Order Model

Giliberti,

Karrenbauer

2021

Preprint

View full text Add to dashboard Cite

The fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical computer science literature so far, although it appears in several applications. Even the previously best known guarantee for the competitive ratio was worse than the best known for the integral problem in the popular random order model. We show that there is an algorithm for the online fractional knapsack problem that admits a competitive ratio of 4.39. Our result significantly improves over the previously best known competitive ratio of 9.37 and surpasses the current best 6.65-competitive algorithm for the integral case. Moreover, our algorithm is deterministic in contrast to the randomized algorithms achieving the results mentioned above. * The work was carried out during a virtual internship at MPI for Informatics.

show abstract

Improved Online Algorithm for Fractional Knapsack in the Random Order Model

Giliberti

Karrenbauer

2021

Approximation and Online Algorithms

View full text Add to dashboard Cite

New results for the k-secretary problem

Cited by 10 publications

References 8 publications

Reading Articles Online

Reading Articles Online

Improved Online Algorithm for Fractional Knapsack in the Random Order Model

Improved Online Algorithm for Fractional Knapsack in the Random Order Model

Contact Info

Product

Resources

About