# A Spectral Approach to Network Design

arXiv: https://arxiv.org/abs/2003.07810 · HTML: https://mlsanity.com/paper/2003.07810/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Experimental Design for Any p-Norm](https://mlsanity.com/paper/2305.01942/) (2023)
- [Experimental Design Using Interlacing Polynomials](https://mlsanity.com/paper/2410.11390/) (2024)

## Abstract (arXiv)

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.