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Correlation Clustering is a classic clustering objective arising in numerous machine learning and data mining applications. Given a graph $G=(V,E)$, the goal is to partition the vertex set into clusters so as to minimize the number of edges…

Data Structures and Algorithms · Computer Science 2024-07-17 Vincent Cohen-Addad , David Rasmussen Lolck , Marcin Pilipczuk , Mikkel Thorup , Shuyi Yan , Hanwen Zhang

For every couple (p;q) of strictly positive integers, the `` alternate congruo-harmonic '' series parametrized by (p;q), whose general term is (-1)^k/(pk+q), converges infra-linearly and very slowly. On the basis of a generalized continued…

Classical Analysis and ODEs · Mathematics 2022-07-06 David Pouvreau

In this paper, we seek a natural problem and a natural distribution of instances such that any $O(n^{c-\epsilon})$-time algorithm fails to solve most instances drawn from the distribution, while the problem admits an $n^{c+o(1)}$-time…

Computational Complexity · Computer Science 2020-10-13 Shuichi Hirahara , Nobutaka Shimizu

Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly convex function $f$ is known to reduce $f({\bf x}_k)-f({\bf x}^*)$ by a factor of $\epsilon\in(0,1)$ after $k=O(\sqrt{L/\ell}\log(1/\epsilon))$ iterations, where…

Optimization and Control · Mathematics 2019-01-11 Sahar Karimi , Stephen Vavasis

Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…

Numerical Analysis · Mathematics 2014-06-27 Aashish Vishwakarma , Murugesan Venkatapathi

We study the average-case version of the Orthogonal Vectors problem, in which one is given as input $n$ vectors from $\{0,1\}^d$ which are chosen randomly so that each coordinate is $1$ independently with probability $p$. Kane and Williams…

Data Structures and Algorithms · Computer Science 2024-10-31 Josh Alman , Alexandr Andoni , Hengjie Zhang

In this paper, an improved GEF fast addition algorithm is proposed. The proposed algorithm reduces time and memory space. In this algorithm, carry is calculated on the basis of arrival timing of the operand's bits without overhead of…

Data Structures and Algorithms · Computer Science 2013-04-09 Md. Mizanur Rahman , Md. Shahadat Hossain , Md. Rakib Hasan , M. M. A. Hashem

Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…

Data Structures and Algorithms · Computer Science 2024-08-27 Scott Wynn , Alec Kyritsis , Stephora Alberi , Enyue Lu

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Optimization and Control · Mathematics 2023-03-07 Mohammadreza Chamanbaz , Roland Bouffanais

We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…

Databases · Computer Science 2020-09-15 Nikolaos Tziavelis , Deepak Ajwani , Wolfgang Gatterbauer , Mirek Riedewald , Xiaofeng Yang

The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…

Information Theory · Computer Science 2020-07-31 Minghui Yang , Keqin Feng

In this work, we show the first worst-case to average-case reduction for the classical $k$-SUM problem. A $k$-SUM instance is a collection of $m$ integers, and the goal of the $k$-SUM problem is to find a subset of $k$ elements that sums to…

Computational Complexity · Computer Science 2020-11-12 Zvika Brakerski , Noah Stephens-Davidowitz , Vinod Vaikuntanathan

This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…

Data Structures and Algorithms · Computer Science 2022-11-16 Mohsen Ghaffari , Christoph Grunau , Slobodan Mitrović

We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…

Hardware Architecture · Computer Science 2007-05-23 Sandeep Sen , Siddhartha Chatterjee , Neeraj Dumir

In this paper, we propose a system combination method for grammatical error correction (GEC), based on nonlinear integer programming (IP). Our method optimizes a novel F score objective based on error types, and combines multiple end-to-end…

Computation and Language · Computer Science 2021-11-03 Ruixi Lin , Hwee Tou Ng

A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…

Data Structures and Algorithms · Computer Science 2024-07-25 Chunyu Luo , Yi Zhou , Zhengren Wang , Mingyu Xiao

Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the…

Quantum Physics · Physics 2019-03-26 Haokun Mao , Qiong Li , Qi Han , Hong Guo

We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for…

Computational Complexity · Computer Science 2018-03-05 Aviad Rubinstein

We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…

Data Structures and Algorithms · Computer Science 2025-05-20 Shi Li , Chenyang Xu , Ruilong Zhang

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only…

Optimization and Control · Mathematics 2011-01-19 Raymond Hemmecke , Shmuel Onn , Robert Weismantel