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arXiv · 2602.09273

The Price of Privacy For Approximating Max-CSP

Prathamesh Dharangutte·Jingcheng Liu·Pasin Manurangsi·Akbar Rafiey·Phanu Vajanopath·Zongrui Zou
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Abstract

We study approximation algorithms for Maximum Constraint Satisfaction Problems (Max-CSPs) under differential privacy (DP) where the constraints are considered sensitive data. Information-theoretically, we aim to classify the best approximation ratios possible for a given privacy budget $\varepsilon$. In the high-privacy regime ($\varepsilon \ll 1$), we show that any $\varepsilon$-DP algorithm cannot beat a random assignment by more than $O(\varepsilon)$ in the approximation ratio. We devise a polynomial-time algorithm which matches this barrier under the assumptions that the instances are bounded-degree and triangle-free. Finally, we show that one or both of these assumptions can be removed for specific CSPs--such as Max-Cut or Max $k$-XOR--albeit at the cost of computational efficiency.

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Prathamesh Dharangutte, Jingcheng Liu, Pasin Manurangsi, Akbar Rafiey, Phanu Vajanopath, Zongrui Zou. 2026-02-09. The Price of Privacy For Approximating Max-CSP. https://arxiv.org/abs/2602.09273

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