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 |...

Full description

Saved in:
Bibliographic Details
Published in:Journal of global optimization Vol. 87; no. 2-4; pp. 917 - 937
Main Authors: Sun, Jian, Zhang, Zan-Bo, Chen, Yannan, Han, Deren, Du, Donglei, Zhang, Xiaoyan
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2023
Springer
Subjects:
Algorithms
Analysis
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Relaxation
Complex semidefinite programming
Randomized algorithm
Approximation algorithm
Max hypergraph 3-cut
ISSN:0925-5001, 1573-2916
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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