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

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 ) into three disjoint subsets V 1 , V 2 , and V 3 such that the sum of edge weights cross different parts is maximized subject to |...

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Bibliographic Details
Published in:Journal of global optimization 2023-11, Vol.87 (2-4), p.917-937
Main Authors: Sun, Jian, Zhang, Zan-Bo, Chen, Yannan, Han, Deren, Du, Donglei, Zhang, Xiaoyan
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Relaxation
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Summary: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 ) into three disjoint subsets V 1 , V 2 , and V 3 such that the sum of edge weights cross different parts is maximized subject to | | V i | - | V l | | ≤ B ( ∀ 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.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01183-7