Mimicking Networks for Constrained Multicuts in Hypergraphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914953319940096 |
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| author | Cho, Kyungjin Oh, Eunjin |
| author_facet | Cho, Kyungjin Oh, Eunjin |
| contents | In this paper, we study a \emph{multicut-mimicking network} for a hypergraph over terminals $T$ with a parameter $c$. It is a hypergraph preserving the minimum multicut values of any set of pairs over $T$ where the value is at most $c$. This is a new variant of the multicut-mimicking network of a graph in [Wahlström ICALP'20], which introduces a parameter $c$ and extends it to handle hypergraphs. Additionally, it is a natural extension of the \emph{connectivity-$c$ mimicking network} introduced by [Chalermsook et al. SODA'21] and [Jiang et al. ESA'22] that is a (hyper)graph preserving the minimum cut values between two subsets of terminals where the value is at most $c$. We propose an algorithm for a hypergraph that returns a multicut-mimicking network over terminals $T$ with a parameter $c$ having $|T|c^{O(r\log c)}$ hyperedges in $p^{1+o(1)}+|T|(c^r\log n)^{\tilde{O}(rc)}m$ time, where $p$ and $r$ are the total size and the rank, respectively, of the hypergraph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mimicking Networks for Constrained Multicuts in Hypergraphs Cho, Kyungjin Oh, Eunjin Data Structures and Algorithms In this paper, we study a \emph{multicut-mimicking network} for a hypergraph over terminals $T$ with a parameter $c$. It is a hypergraph preserving the minimum multicut values of any set of pairs over $T$ where the value is at most $c$. This is a new variant of the multicut-mimicking network of a graph in [Wahlström ICALP'20], which introduces a parameter $c$ and extends it to handle hypergraphs. Additionally, it is a natural extension of the \emph{connectivity-$c$ mimicking network} introduced by [Chalermsook et al. SODA'21] and [Jiang et al. ESA'22] that is a (hyper)graph preserving the minimum cut values between two subsets of terminals where the value is at most $c$. We propose an algorithm for a hypergraph that returns a multicut-mimicking network over terminals $T$ with a parameter $c$ having $|T|c^{O(r\log c)}$ hyperedges in $p^{1+o(1)}+|T|(c^r\log n)^{\tilde{O}(rc)}m$ time, where $p$ and $r$ are the total size and the rank, respectively, of the hypergraph. |
| title | Mimicking Networks for Constrained Multicuts in Hypergraphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.12548 |