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Mimicking Networks for Constrained Multicuts in Hypergraphs

Authors Kyungjin Cho , Eunjin Oh

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ACM Subject Classification
  • Theory of computation → Sparsification and spanners
Keywords
  • hyperedge multicut
  • vertex sparsification
  • parameterized complexity

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Abstract

In this paper, we study a 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 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(rlog c) hyperedges in p^{1+o(1)} + |T|(c^rlog n)^{Õ(rc)}⋅m time, where p and r are the total size and the rank, respectively, of the hypergraph.

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Kyungjin Cho and Eunjin Oh. Mimicking Networks for Constrained Multicuts in Hypergraphs. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.21

Author Details

Kyungjin Cho
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Eunjin Oh
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea

Funding

This work was partly supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.RS-2024-00440239, Sublinear Scalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.RS-2024-00358505).
  • Cho, Kyungjin: Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.RS-2024-00410835).

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