English
Related papers

Related papers: Reverse Greedy is Bad for k-Center

200 papers

We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the…

Numerical Analysis · Mathematics 2024-10-29 Yuwen Li , Jonathan Siegel

The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…

Functional Analysis · Mathematics 2025-06-24 Brody Dylan Johnson

A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…

Data Structures and Algorithms · Computer Science 2025-07-18 Chenhao Wang

Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the…

Machine Learning · Computer Science 2024-05-03 Yue Wang , Yi Zhou , Shaofeng Zou

We show that the greedy algorithm for adaptive-submodular cover has approximation ratio at least 1.3*(1+ln Q). Moreover, the instance demonstrating this gap has Q=1. So, it invalidates a prior result in the paper ``Adaptive Submodularity: A…

Data Structures and Algorithms · Computer Science 2024-05-27 Blake Harris , Viswanath Nagarajan

We study sparse approximation by greedy algorithms. Our contribution is two-fold. First, we prove exact recovery with high probability of random $K$-sparse signals within $\lceil K(1+\e)\rceil$ iterations of the Orthogonal Matching Pursuit…

Numerical Analysis · Mathematics 2013-04-03 Eugene Livshitz , Vladimir Temlyakov

In a metric space, a set of point sets of roughly the same size and an integer $k\geq 1$ are given as the input and the goal of data-distributed $k$-center is to find a subset of size $k$ of the input points as the set of centers to…

Computational Geometry · Computer Science 2023-09-11 Sepideh Aghamolaei , Mohammad Ghodsi

Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were…

Data Structures and Algorithms · Computer Science 2022-11-08 Georg Anegg , Laura Vargas Koch , Rico Zenklusen

We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…

Numerical Analysis · Mathematics 2020-12-02 Guy Leibovitz , Raja Giryes

In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence…

Probability · Mathematics 2013-10-18 Tamas Szantai , Edith Kovacs

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…

Machine Learning · Statistics 2014-12-11 Vladimir Temlyakov

We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…

Data Structures and Algorithms · Computer Science 2025-03-26 Matthijs Ebbens , Nicole Funk , Jan Höckendorff , Christian Sohler , Vera Weil

Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of…

Data Structures and Algorithms · Computer Science 2013-08-26 Gagan Goel , Pushkar Tripathi

Motivated by applications in online dating and kidney exchange, the stochastic matching problem was introduced by Chen, Immorlica, Karlin, Mahdian and Rudra (2009). They have proven a 4-approximation of a simple greedy strategy, but…

Data Structures and Algorithms · Computer Science 2013-11-06 Marek Adamczyk

The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy…

Discrete Mathematics · Computer Science 2019-01-18 Sebastian Siebertz

We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t>1. We also supply a method for constructing some permutations that can be sorted by t…

Combinatorics · Mathematics 2007-05-23 Rebecca Smith

Closeness is a widely-used centrality measure in social network analysis. For a node it indicates the reciprocal of the average shortest-path distance to the other nodes of the network. While the identification of the k nodes with highest…

Data Structures and Algorithms · Computer Science 2019-05-16 Elisabetta Bergamini , Tanya Gonser , Henning Meyerhenke

We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…

Data Structures and Algorithms · Computer Science 2022-06-28 Soheil Behnezhad , Mohammad Roghani , Aviad Rubinstein , Amin Saberi

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem…

Data Structures and Algorithms · Computer Science 2015-12-08 Gabriele Fici , Tomasz Kociumaka , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń

The rate of convergence of the classical Thresholding Greedy Algorithm with respect to bases is studied in this paper. We bound the error of approximation by the product of both norms -- the norm of $f$ and the $A_1$-norm of $f$. We obtain…

Numerical Analysis · Mathematics 2024-07-29 V. N. Temlyakov