Streaming Max-Cut in General Metrics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917449281044480 |
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| author | Jiang, Shaofeng H. -C. Peng, Pan Wang, Haoze |
| author_facet | Jiang, Shaofeng H. -C. Peng, Pan Wang, Haoze |
| contents | Max-Cut is a fundamental combinatorial optimization problem that has been studied in various computational settings. We initiate the study of its streaming complexity in \emph{general metric spaces} with access to distance oracles. We give a $(1 + ε)$-approximate algorithm for estimating the Max-Cut value in \emph{sliding-window} streams using only poly-logarithmic space. This is the first sliding-window algorithm for Max-Cut even in Euclidean spaces, and it matches a known insertion-only space bound in the special case of Euclidean spaces [Chen, Jiang, Krauthgamer, STOC'23]. In sharp contrast, we give a $\poly(n)$-space lower bound in the \emph{dynamic} streaming setting. This yields a separation from the Euclidean case, where the polylogarithmic-space $(1+ε)$-approximation extends to dynamic streams.
On the technical side, our sliding-window algorithm builds on the smooth histogram framework of [Braverman and Ostrovsky, SICOMP'10]. To make this framework applicable, we establish the first smoothness bound for metric Max-Cut. Moreover, we develop a streaming algorithm for metric Max-Cut in insertion-only streams, whose key ingredient is a new metric reservoir sampling technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Streaming Max-Cut in General Metrics Jiang, Shaofeng H. -C. Peng, Pan Wang, Haoze Data Structures and Algorithms Max-Cut is a fundamental combinatorial optimization problem that has been studied in various computational settings. We initiate the study of its streaming complexity in \emph{general metric spaces} with access to distance oracles. We give a $(1 + ε)$-approximate algorithm for estimating the Max-Cut value in \emph{sliding-window} streams using only poly-logarithmic space. This is the first sliding-window algorithm for Max-Cut even in Euclidean spaces, and it matches a known insertion-only space bound in the special case of Euclidean spaces [Chen, Jiang, Krauthgamer, STOC'23]. In sharp contrast, we give a $\poly(n)$-space lower bound in the \emph{dynamic} streaming setting. This yields a separation from the Euclidean case, where the polylogarithmic-space $(1+ε)$-approximation extends to dynamic streams. On the technical side, our sliding-window algorithm builds on the smooth histogram framework of [Braverman and Ostrovsky, SICOMP'10]. To make this framework applicable, we establish the first smoothness bound for metric Max-Cut. Moreover, we develop a streaming algorithm for metric Max-Cut in insertion-only streams, whose key ingredient is a new metric reservoir sampling technique. |
| title | Streaming Max-Cut in General Metrics |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.04435 |