# Approximation algorithms for the maximally balanced connected graph tripartition problem

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2020-02-17

AUTHORS ABSTRACT

Given a vertex-weighted connected graph G=(V,E,w(·))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E, w(\cdot ))$$\end{document}, the maximally balanced connected graphk-partition (k-BGP) seeks to partition the vertex set V into k non-empty parts such that the subgraph induced by each part is connected and the weights of these k parts are as balanced as possible. When the concrete objective is to maximize the minimum (to minimize the maximum, respectively) weight of the k parts, the problem is denoted as max–mink-BGP (min–maxk-BGP, respectively), and has received much study since about four decades ago. On general graphs, max–mink-BGP is strongly NP-hard for every fixed k≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \ge 2$$\end{document}, and remains NP-hard even for the vertex uniformly weighted case; when k is part of the input, the problem is denoted as max–min BGP, and cannot be approximated within 6/5 unless P =\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=$$\end{document} NP. In this paper, we study the tripartition problems from approximation algorithms perspective and present a 3/2-approximation for min–max 3-BGP and a 5/3-approximation for max–min 3-BGP, respectively. These are the first non-trivial approximation algorithms for 3-BGP, to our best knowledge. More... »

PAGES

1-21

### References to SciGraph publications

• 2019-11-23. Approximation Algorithms for Maximally Balanced Connected Graph Partition in COMBINATORIAL OPTIMIZATION AND APPLICATIONS
• 2017-07-05. The Complexity of Tree Partitioning in ALGORITHMS AND DATA STRUCTURES
• 2011. A 7/6-Approximation Algorithm for the Max-Min Connected Bipartition Problem on Grid Graphs in COMPUTATIONAL GEOMETRY, GRAPHS AND APPLICATIONS
• 1977-09. A homology theory for spanning tress of a graph in ACTA MATHEMATICA HUNGARICA
• 2018-03-21. Efficient Algorithms for a Graph Partitioning Problem in FRONTIERS IN ALGORITHMICS
• 2013-01-03. Max-min weight balanced connected partition in JOURNAL OF GLOBAL OPTIMIZATION
• ### Journal

TITLE

Journal of Combinatorial Optimization

ISSUE

N/A

VOLUME

N/A

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10878-020-00544-w

DOI

http://dx.doi.org/10.1007/s10878-020-00544-w

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https://app.dimensions.ai/details/publication/pub.1124916632

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