Improved Online Algorithms for Knapsack and GAP in the Random Order Model

Albers, Susanne; Khan, Arindam; Ladewig, Leon

doi:10.4230/lipics.approx-random.2019.22

Cited by 4 publications

(6 citation statements)

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“…Given an αcompetitive algorithm for the Online Knapsack Problem as a black box, we obtain a (e + α)C-competitive algorithm for RAO. This algorithm is 3.45eCcompetitive when using the current best algorithm for the Online Knapsack Problem from [2]. This is the current best upper bound that we can show for RAO, which is constant provided that the hints admit a constant accuracy.…”

Section: Our Contributionmentioning

confidence: 67%

“…To the best of our knowledge, the problem of RAO has not been studied in our suggested setting yet. The closest related problem known is the Online Knapsack Problem [2,4,10] in which an algorithm has to fill a knapsack with restricted capacity while trying to maximize the sum of the items' values. Since the input is not known at the beginning and an item is not selectable later than its arrival, optimal algorithms do not exist.…”

Section: Related Workmentioning

confidence: 99%

“…An 8.06-competitive algorithm (8.06 < 2.97e) is shown in [10] for the Generalized Assignment Problem, which is the Online Knapsack Problem generalized to a setting with multiple knapsacks with different capacities. The current best algorithm from [2] achieves a competitive ratio of 6.65 < 2.45e.…”

Section: Related Workmentioning

confidence: 99%

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Reading Articles Online

Karrenbauer¹,

Kovalevskaya²

2020

Combinatorial Optimization and Applications

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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.

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Section: Our Contributionmentioning

confidence: 67%

Section: Related Workmentioning

confidence: 99%

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Reading Articles Online

Karrenbauer¹,

Kovalevskaya²

2020

Combinatorial Optimization and Applications

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“…The hardness of the variants with arbitrary profits and sizes as well as applications to online auctions motivated another strand of research focused on the so-called random-order model [1,3,15,19]. There, the set of items is chosen adversarially, but the items are presented to an online algorithm in random order.…”

Section: Related Workmentioning

confidence: 99%

“…max{f(y), thr(M S )} dy. Particular subsets of L + are depicted in Figure 3 (right); the removed part of gain T * is depicted as (1).…”

Section: Thus G(lmentioning

confidence: 99%

An Optimal Algorithm for Online Multiple Knapsack

Bienkowski,

Pacut,

Piecuch

2020

Preprint

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In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of n bins (knapsacks) of equal size. The gain of an algorithm is equal to the sum of sizes of accepted items and the goal is to maximize the total gain.So far, for this natural problem, the best solution was the 0.5-competitive algorithm FirstFit (the result holds for any n ≥ 2). We present the first algorithm that beats this ratio, achieving the competitive ratio of 1/(1 + ln( 2Our algorithm is deterministic and optimal up to lower-order terms, as the upper bound of 1/(1 + ln(2)) for randomized solutions was given previously by Cygan et al. [TOCS 2016].

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Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Böhm¹,

Éberlé²,

Megow³

et al. 2021

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Improved Online Algorithms for Knapsack and GAP in the Random Order Model

Cited by 4 publications

References 0 publications

Reading Articles Online

Reading Articles Online

An Optimal Algorithm for Online Multiple Knapsack

Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

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