### Abstract

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

Original language | English (US) |
---|---|

Pages (from-to) | 57-71 |

Number of pages | 15 |

Journal | Journal of Global Optimization |

Volume | 48 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bipartite graph partitioning
- Graph partitioning
- Linear programming
- Quadratic programming

### ASJC Scopus subject areas

- Computer Science Applications
- Control and Optimization
- Applied Mathematics
- Management Science and Operations Research

### Cite this

*Journal of Global Optimization*,

*48*(1), 57-71. https://doi.org/10.1007/s10898-009-9520-1

**Linear and quadratic programming approaches for the general graph partitioning problem.** / Fan, Neng; Pardalos, Panos M.

Research output: Contribution to journal › Article

*Journal of Global Optimization*, vol. 48, no. 1, pp. 57-71. https://doi.org/10.1007/s10898-009-9520-1

}

TY - JOUR

T1 - Linear and quadratic programming approaches for the general graph partitioning problem

AU - Fan, Neng

AU - Pardalos, Panos M.

PY - 2010/9

Y1 - 2010/9

N2 - The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

AB - The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

KW - Bipartite graph partitioning

KW - Graph partitioning

KW - Linear programming

KW - Quadratic programming

UR - http://www.scopus.com/inward/record.url?scp=77955510847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955510847&partnerID=8YFLogxK

U2 - 10.1007/s10898-009-9520-1

DO - 10.1007/s10898-009-9520-1

M3 - Article

VL - 48

SP - 57

EP - 71

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 1

ER -