Approximation Algorithms for Noncommutative CSPs

Noncommutative constraint satisfaction problems (CSPs) are higher-dimensional operator extensions of classical CSPs. Their approximability remains largely unexplored. A notable example of a noncommutative CSP that is not solvable in polynomial time is NC-Max-3-Cut. We present a 0.864-approximation a...

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Bibliographic Details
Published inProceedings / annual Symposium on Foundations of Computer Science pp. 920 - 929
Main Authors Culf, Eric, Mousavi, Hamoon, Spirig, Taro
Format Conference Proceeding
LanguageEnglish
Published IEEE 27.10.2024
Subjects
Approximation algorithms
Computer science
constraint satisfaction problems
noncommutative polynomial optimization
Polynomials
quantum complexity
Quantum computing
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ISSN2575-8454
DOI10.1109/FOCS61266.2024.00061

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Summary:Noncommutative constraint satisfaction problems (CSPs) are higher-dimensional operator extensions of classical CSPs. Their approximability remains largely unexplored. A notable example of a noncommutative CSP that is not solvable in polynomial time is NC-Max-3-Cut. We present a 0.864-approximation algorithm for this problem. Our approach extends to a broader class of both classical and noncommutative CSPs. We introduce three key concepts: approximate isometry, relative distribution, and generalized anticommutation, which may be of independent interest.
ISSN:2575-8454
DOI:10.1109/FOCS61266.2024.00061