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

Jian Sun, Zan-Bo Zhang, Yannan Chen, Deren Han, Donglei Du and Xiaoyan Zhang ()
Additional contact information
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

Journal of Global Optimization, 2023, vol. 87, issue 2, No 25, 917-937

Abstract: 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.

Keywords: Randomized algorithm; Approximation algorithm; Complex semidefinite programming; Max hypergraph 3-cut (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01183-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01183-7

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01183-7

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().