Deterministic Edge Connectivity and Max Flow using Subquadratic Cut Queries
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917814404644864 |
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| author | Anand, Aditya Saranurak, Thatchaphol Wang, Yunfan |
| author_facet | Anand, Aditya Saranurak, Thatchaphol Wang, Yunfan |
| contents | We give the first deterministic algorithm that makes sub-quadratic queries to find the global min-cut of a simple graph in the cut query model. Given an $n$-vertex graph $G$, our algorithm makes $\widetilde{O}(n^{5/3})$ queries to compute the global min-cut in $G$. As a key ingredient, we also show an algorithm for finding $s$-$t$ max-flows of size $\widetilde{O}(n)$ in $\widetilde{O}(n^{5/3})$ queries. We also show efficient cut-query implementations of versions of expander decomposition and isolating cuts, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deterministic Edge Connectivity and Max Flow using Subquadratic Cut Queries Anand, Aditya Saranurak, Thatchaphol Wang, Yunfan Data Structures and Algorithms We give the first deterministic algorithm that makes sub-quadratic queries to find the global min-cut of a simple graph in the cut query model. Given an $n$-vertex graph $G$, our algorithm makes $\widetilde{O}(n^{5/3})$ queries to compute the global min-cut in $G$. As a key ingredient, we also show an algorithm for finding $s$-$t$ max-flows of size $\widetilde{O}(n)$ in $\widetilde{O}(n^{5/3})$ queries. We also show efficient cut-query implementations of versions of expander decomposition and isolating cuts, which may be of independent interest. |
| title | Deterministic Edge Connectivity and Max Flow using Subquadratic Cut Queries |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.18704 |