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A Spectral Approach to Network Design
- Source :
- STOC
- Publication Year :
- 2022
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2022.
-
Abstract
- 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.<br />Comment: Improved bound on one-sided spectral rounding by a randomized swapping algorithm. Added the proof of the deterministic algorithm for additive sparsifers
- Subjects :
- FOS: Computer and information sciences
0209 industrial biotechnology
Spectral approach
Scope (project management)
General Computer Science
Property (programming)
Computer science
Rounding
General Mathematics
Approximation algorithm
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Network planning and design
020901 industrial engineering & automation
010201 computation theory & mathematics
Computer Science - Data Structures and Algorithms
Data Structures and Algorithms (cs.DS)
Randomized rounding
Algorithm
Discrepancy theory
Subjects
Details
- ISSN :
- 10957111 and 00975397
- Volume :
- 51
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Computing
- Accession number :
- edsair.doi.dedup.....d6594a9637b8ea55bf1d53da1cc7d073