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Related papers: The $(h,k)$-Server Problem on Bounded Depth Trees

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In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…

Data Structures and Algorithms · Computer Science 2021-10-28 Susanne Albers , Waldo Gálvez , Maximilian Janke

In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a…

Data Structures and Algorithms · Computer Science 2019-06-12 Moran Feldman , Ran Haba

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find…

Data Structures and Algorithms · Computer Science 2020-05-29 Marek Chrobak , Claire Kenyon , John Noga , Neal E. Young

We give a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending…

Data Structures and Algorithms · Computer Science 2025-07-09 Afrouz Jabal Ameli , Laura Sanita , Moritz Venzin

In this paper we study the hardness of the $k$-Center problem on inputs that model transportation networks. For the problem, a graph $G=(V,E)$ with edge lengths and an integer $k$ are given and a center set $C\subseteq V$ needs to be chosen…

Computational Complexity · Computer Science 2020-03-03 Andreas Emil Feldmann , Daniel Marx

We introduce the problem of $k$-chasing of convex functions, a simultaneous generalization of both the famous k-server problem in $R^d$, and of the problem of chasing convex bodies and functions. Aside from fundamental interest in this…

Data Structures and Algorithms · Computer Science 2020-04-17 Sébastien Bubeck , Yuval Rabani , Mark Sellke

The deterministic $k$-server conjecture states that there is a $k$-competitive deterministic algorithm for the $k$-server problem for any metric space. We show that the work function algorithm is $3$-competitive for the $3$-server problem…

Data Structures and Algorithms · Computer Science 2022-05-18 Zhiyi Huang , Hanwen Zhang

We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem. For the…

Data Structures and Algorithms · Computer Science 2020-11-30 Sébastien Bubeck , Michael B. Cohen , James R. Lee , Yin Tat Lee

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…

Data Structures and Algorithms · Computer Science 2011-02-25 Anupam Gupta , Viswanath Nagarajan , R. Ravi

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of…

Data Structures and Algorithms · Computer Science 2024-07-09 S M Ferdous , Bhargav Samineni , Alex Pothen , Mahantesh Halappanavar , Bala Krishnamoorthy

This paper provides a systematic study of several proposed measures for online algorithms in the context of a specific problem, namely, the two server problem on three colinear points. Even though the problem is simple, it encapsulates a…

Data Structures and Algorithms · Computer Science 2012-10-15 Joan Boyar , Sandy Irani , Kim S. Larsen

We consider the Work Function Algorithm for the k-server problem. We show that if the Work Function Algorithm is c-competitive, then it is also strictly (2c)-competitive. As a consequence of [Koutsoupias and Papadimitriou, JACM 1995] this…

Data Structures and Algorithms · Computer Science 2009-02-10 Yuval Emek , Pierre Fraigniaud , Amos Korman , Adi Rosen

The generalized 2-server problem is an online optimization problem where a sequence of requests has to be served at minimal cost. Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the…

Data Structures and Algorithms · Computer Science 2013-11-28 Rene Sitters

k-means is a widely used clustering algorithm, but for $k$ clusters and a dataset size of $N$, each iteration of Lloyd's algorithm costs $O(kN)$ time. Although there are existing techniques to accelerate single Lloyd iterations, none of…

Data Structures and Algorithms · Computer Science 2016-01-18 Ryan R. Curtin

We consider a multi-level aggregation problem in a weighted rooted tree, studied recently by Bienkowski et al. (2015). In this problem requests arrive over time at the nodes of the tree, and each request specifies a deadline. A request is…

Data Structures and Algorithms · Computer Science 2017-01-10 Niv Buchbinder , Moran Feldman , Joseph Naor , Ohad Talmon

We consider the online bipartite matching problem on $(k,d)$-bounded graphs, where each online vertex has at most $d$ neighbors, each offline vertex has at least $k$ neighbors, and $k\geq d\geq 2$. The model of $(k,d)$-bounded graphs is…

Data Structures and Algorithms · Computer Science 2023-12-05 Yilong Feng , Xiaowei Wu , Shengwei Zhou

We consider online algorithms for the $k$-server problem on trees. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, a naive implementation of their algorithm has…

Data Structures and Algorithms · Computer Science 2021-07-29 Ruslan Kapralov , Kamil Khadiev , Joshua Mokut , Yixin Shen , Maxim Yagafarov

Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top $K$ items from noisy pairwise comparisons. In our setting, we are non-actively given $r$…

Data Structures and Algorithms · Computer Science 2016-05-13 Xi Chen , Sivakanth Gopi , Jieming Mao , Jon Schneider

We consider the following online optimization problem. We are given a graph $G$ and each vertex of the graph is assigned to one of $\ell$ servers, where servers have capacity $k$ and we assume that the graph has $\ell \cdot k$ vertices.…

Data Structures and Algorithms · Computer Science 2020-11-03 Monika Henzinger , Stefan Neumann , Harald Räcke , Stefan Schmid

Computing bounded depth decompositions is a bottleneck in many applications of the treedepth parameter. The fastest known algorithm, which is due to Reidl, Rossmanith, S\'{a}nchez Villaamil, and Sikdar [ICALP 2014], runs in…

Data Structures and Algorithms · Computer Science 2025-02-25 Lars Jaffke , Paloma T. de Lima , Wojciech Nadara , Emmanuel Sam