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In the online general knapsack problem, an algorithm is presented with an item $x=(s,v)$ of size $s$ and value $v$ and must irrevocably choose to pack such an item into the knapsack or reject it before the next item appears. The goal is to…

Data Structures and Algorithms · Computer Science 2025-04-30 Elisabet Burjons , Matthias Gehnen

Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…

Data Structures and Algorithms · Computer Science 2024-04-03 Calum MacRury , Will Ma , Nathaniel Grammel

Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the…

Data Structures and Algorithms · Computer Science 2018-10-19 Zhiyi Huang , Binghui Peng , Zhihao Gavin Tang , Runzhou Tao , Xiaowei Wu , Yuhao Zhang

The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class,…

Data Structures and Algorithms · Computer Science 2016-05-26 Joan Boyar , Lene M. Favrholdt , Christian Kudahl , Jesper W. Mikkelsen

We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…

Data Structures and Algorithms · Computer Science 2012-11-01 Elisabeth Günther , Olaf Maurer , Nicole Megow , Andreas Wiese

We give a polynomial-time algorithm for OnlineSetCover with a competitive ratio of $O(\log mn)$ when the elements are revealed in random order, essentially matching the best possible offline bound of $O(\log n)$ and circumventing the…

Data Structures and Algorithms · Computer Science 2024-07-09 Anupam Gupta , Gregory Kehne , Roie Levin

Search engines answer users' queries by listing relevant items (e.g. documents, songs, products, web pages, ...). These engines rely on algorithms that learn to rank items so as to present an ordered list maximizing the probability that it…

Machine Learning · Computer Science 2021-09-14 Stefan Magureanu , Alexandre Proutiere , Marcus Isaksson , Boxun Zhang

We extend the standard online worst-case model to accommodate past experience which is available to the online player in many practical scenarios. We do this by revealing a random sample of the adversarial input to the online player ahead…

Data Structures and Algorithms · Computer Science 2019-07-12 Haim Kaplan , David Naori , Danny Raz

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary…

Optimization and Control · Mathematics 2025-01-27 Ruicheng Ao , Jiashuo Jiang , David Simchi-Levi

Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…

Data Structures and Algorithms · Computer Science 2020-06-11 Martin Olsen , Allan Gross

We consider an online learning to rank setting in which, at each round, an oblivious adversary generates a list of $m$ documents, pertaining to a query, and the learner produces scores to rank the documents. The adversary then generates a…

Machine Learning · Computer Science 2016-08-24 Sougata Chaudhuri , Ambuj Tewari

We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…

Data Structures and Algorithms · Computer Science 2015-08-06 Marc P. Renault , Adi Rosén , Rob van Stee

We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a…

Data Structures and Algorithms · Computer Science 2023-03-28 Benjamin Moseley , Heather Newman , Kirk Pruhs

We introduce algorithms for online, full-information prediction that are competitive with contextual tree experts of unknown complexity, in both probabilistic and adversarial settings. We show that by incorporating a probabilistic framework…

Machine Learning · Computer Science 2018-05-23 Vidya Muthukumar , Mitas Ray , Anant Sahai , Peter L. Bartlett

We revisit the online bipartite matching problem on $d$-regular graphs, for which Cohen and Wajc (SODA 2018) proposed an algorithm with a competitive ratio of $1-2\sqrt{H_d/d} = 1-O(\sqrt{(\log d)/d})$ and showed that it is asymptotically…

Data Structures and Algorithms · Computer Science 2025-10-02 Yilong Feng , Haolong Li , Xiaowei Wu , Shengwei Zhou

In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…

Data Structures and Algorithms · Computer Science 2007-05-23 Ming-Yang Kao , Stephen R. Tate

The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of…

Data Structures and Algorithms · Computer Science 2017-01-10 Jhoirene Clemente , Juraj Hromkovic , Dennis Komm , Christian Kudahl

We explore a novel problem in streaming submodular maximization, inspired by the dynamics of news-recommendation platforms. We consider a setting where users can visit a news website at any time, and upon each visit, the website must…

Data Structures and Algorithms · Computer Science 2026-01-19 Honglian Wang , Sijing Tu , Lutz Oettershagen , Aristides Gionis

In evaluating an algorithm, worst-case analysis can be overly pessimistic. Average-case analysis can be overly optimistic. An intermediate approach is to show that an algorithm does well on a broad class of input distributions. Koutsoupias…

Data Structures and Algorithms · Computer Science 2015-06-02 Neal E. Young

We study the online maximum coverage problem on a line, in which, given an online sequence of sub-intervals (which may intersect among each other) of a target large interval and an integer $k$, we aim to select at most $k$ of the…

Data Structures and Algorithms · Computer Science 2020-11-24 Songhua Li , Minming Li , Lingjie Duan , Victor C. S. Lee