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A maximum hypergraph 3-cut problem with limited unbalance: approximation and analysis

Author

Listed:
  • Jian Sun

    (Beijing University of Technology)

  • Zan-Bo Zhang

    (Guangdong University of Finance and Economics)

  • Yannan Chen

    (South China Normal University)

  • Deren Han

    (Beihang University)

  • Donglei Du

    (University of New Brunswick)

  • Xiaoyan Zhang

    (Nanjing Normal University)

Abstract

We consider the max hypergraph 3-cut problem with limited unbalance (MH3C-LU). The objective is to divide the vertex set of an edge-weighted hypergraph $$H=(V,E,w)$$ H = ( V , E , w ) into three disjoint subsets $$V_{1}$$ V 1 , $$V_{2}$$ V 2 , and $$V_{3}$$ V 3 such that the sum of edge weights cross different parts is maximized subject to $$||V_{i}|-|V_{l}||\le B$$ | | V i | - | V l | | ≤ B ( $$\forall i\ne l\in \{1,2,3\}$$ ∀ i ≠ l ∈ { 1 , 2 , 3 } ) for a given parameter B. This problem is NP-hard because it includes some well-known problems like the max 3-section problem and the max 3-cut problem as special cases. We formulate the MH3C-LU as a ternary quadratic program and present a randomized approximation algorithm based on the complex semidefinite programming relaxation technique.

Suggested Citation

  • Jian Sun & Zan-Bo Zhang & Yannan Chen & Deren Han & Donglei Du & Xiaoyan Zhang, 2023. "A maximum hypergraph 3-cut problem with limited unbalance: approximation and analysis," Journal of Global Optimization, Springer, vol. 87(2), pages 917-937, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01183-7
    DOI: 10.1007/s10898-022-01183-7
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