组合科学计算中的近似算法

IF 16.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2019-05-01 DOI:10.1017/S0962492919000035

A. Pothen, S. Ferdous, F. Manne

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引用次数: 16

摘要

本文综述了近年来计算图中度约束子图的近似算法及其在组合科学计算中的应用。我们考虑的问题包括基数匹配、边缘加权匹配、顶点加权匹配和边缘加权$b$匹配的最大化版本，以及加权边缘覆盖和$b$边缘覆盖的最小化版本。这些问题的精确算法对于具有数百万条边的海量图来说是不切实际的。对于每个问题，我们讨论了理论基础，几种线性或近线性时间逼近算法的设计，它们在串行和并行计算机上的实现，以及应用。我们的重点是在具有多线程和互联处理器的现代计算机体系结构上产生良好性能的实用算法。我们还提供了有关这些问题可用的软件的信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Approximation algorithms in combinatorial scientific computing

We survey recent work on approximation algorithms for computing degree-constrained subgraphs in graphs and their applications in combinatorial scientific computing. The problems we consider include maximization versions of cardinality matching, edge-weighted matching, vertex-weighted matching and edge-weighted $b$ -matching, and minimization versions of weighted edge cover and $b$ -edge cover. Exact algorithms for these problems are impractical for massive graphs with several millions of edges. For each problem we discuss theoretical foundations, the design of several linear or near-linear time approximation algorithms, their implementations on serial and parallel computers, and applications. Our focus is on practical algorithms that yield good performance on modern computer architectures with multiple threads and interconnected processors. We also include information about the software available for these problems.

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来源期刊

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.