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Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

Optimization and Control · Mathematics 2022-11-01 Rahul Mazumder , Haoyue Wang

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…

Computation · Statistics 2018-10-18 Simon Bartels , Jon Cockayne , Ilse C. F. Ipsen , Philipp Hennig

Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…

Data Structures and Algorithms · Computer Science 2023-06-16 Daniel Anderson , Guy E. Blelloch

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

Numerical Analysis · Mathematics 2023-12-13 Johannes J. Brust , Michael A. Saunders

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…

Numerical Analysis · Mathematics 2020-09-16 Daniel Boley

Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's pioneering 1969 paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-07-16 Haim Avron , Alex Druinsky , Anshul Gupta

Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…

Numerical Analysis · Mathematics 2012-06-11 Oren E. Livne , Achi Brandt

Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…

Combinatorics · Mathematics 2021-08-19 Maciej Bendkowski , Olivier Bodini , Sergey Dovgal

In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring…

Data Structures and Algorithms · Computer Science 2017-08-22 Michael B. Cohen , Aleksander Madry , Dimitris Tsipras , Adrian Vladu

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

Methodology · Statistics 2021-09-13 Sören R. Künzel , Theo F. Saarinen , Edward W. Liu , Jasjeet S. Sekhon

This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…

Optimization and Control · Mathematics 2017-02-28 Kin Cheong Sou , Jie Lu

Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…

Data Structures and Algorithms · Computer Science 2020-03-17 MohammadTaghi Hajiaghayi , Masoud Seddighin , Saeed Seddighin , Xiaorui Sun

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…

Data Structures and Algorithms · Computer Science 2023-04-11 Matthew Fahrbach , Gary L. Miller , Richard Peng , Saurabh Sawlani , Junxing Wang , Shen Chen Xu

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…

Data Structures and Algorithms · Computer Science 2015-06-02 Samir Khuller , Balaji Raghavachari , Neal E. Young

Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

Data Structures and Algorithms · Computer Science 2021-11-23 Aviad Rubinstein , Saeed Seddighin , Zhao Song , Xiaorui Sun

Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin's method, can be viewed as an iterative method that…

Numerical Analysis · Mathematics 2018-10-30 Jamie Haddock , Deanna Needell

Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…

Data Structures and Algorithms · Computer Science 2023-09-14 Sally Dong , Yin Tat Lee , Guanghao Ye

We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…

Data Structures and Algorithms · Computer Science 2015-08-19 Jens Maßberg