We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in discrepancy theory. We extend these results to incorporate additional non-negative linear constraints, and show that they can be used to significantly extend the scope of network design problems that can be solved. Our algorithm for spectral rounding is an iterative randomized rounding algorithm based on the regret minimization framework. In some settings, this provides an alternative spectral algorithm to achieve constant factor approximation for the classical survivable network design problem, and partially answers a question of Bansal about survivable network design with concentration property. We also show many other applications of the spectral rounding results, including weighted experimental design and additive spectral sparsification.

中文翻译：

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网络设计的光谱方法

我们提出了一种谱方法来设计网络设计问题的近似算法。我们观察到潜在的数学问题是谱舍入问题，在谱稀疏化和差异理论中进行了研究。我们扩展这些结果以包含额外的非负线性约束，并表明它们可用于显着扩展可解决的网络设计问题的范围。我们的频谱舍入算法是一种基于遗憾最小化框架的迭代随机舍入算法。在某些情况下，这提供了一种替代谱算法来实现经典可生存网络设计问题的常数因子近似，并部分回答了 Bansal 关于具有集中属性的可生存网络设计的问题。