A Spectral Approach to Network Design
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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 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 survivable network design, and partially answers a question of Bansal about survivable network design with concentration property. We also show that the spectral rounding results have many other applications, including weighted experimental design and additive spectral sparsification.
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