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.

中文翻译：

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组合科学计算中的逼近算法

我们调查了最近关于计算图中度数约束子图的近似算法及其在组合科学计算中的应用的工作。我们考虑的问题包括基数匹配、边加权匹配、顶点加权匹配和边加权的最大化版本$b$-加权边缘覆盖的匹配和最小化版本和$b$-边缘覆盖。这些问题的精确算法对于具有数百万条边的海量图是不切实际的。对于每个问题，我们都会讨论理论基础、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连处理器的现代计算机架构上产生良好性能的实用算法。我们还包括有关可用于这些问题的软件的信息。