### Abstract

Original language | English |
---|---|

Pages (from-to) | 143-154 |

Journal | Annals of Operations Research |

Volume | 265 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 2018 |

### Fingerprint

### Keywords

- graph bisection
- graph partition
- semidefinite programming
- boolean quadratic polytope

### Cite this

*Annals of Operations Research*,

*265*(1), 143-154. https://doi.org/10.1007/s10479-017-2575-3

}

*Annals of Operations Research*, vol. 265, no. 1, pp. 143-154. https://doi.org/10.1007/s10479-017-2575-3

**Graph bisection revisited.** / Sotirov, Renata.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Graph bisection revisited

AU - Sotirov, Renata

PY - 2018/6

Y1 - 2018/6

N2 - The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of order n—the number of vertices of the graph—that is equivalent to the currently strongest semidefinite programming relaxation obtained by using vector lifting. The reduction in the size of the matrix variable enables us to impose additional valid inequalities to the relaxation in order to further strengthen it. The numerical results confirm that our simplified and strengthened semidefinite relaxation provides the currently strongest bound for the graph bisection problem in reasonable time.

AB - The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of order n—the number of vertices of the graph—that is equivalent to the currently strongest semidefinite programming relaxation obtained by using vector lifting. The reduction in the size of the matrix variable enables us to impose additional valid inequalities to the relaxation in order to further strengthen it. The numerical results confirm that our simplified and strengthened semidefinite relaxation provides the currently strongest bound for the graph bisection problem in reasonable time.

KW - graph bisection

KW - graph partition

KW - semidefinite programming

KW - boolean quadratic polytope

U2 - 10.1007/s10479-017-2575-3

DO - 10.1007/s10479-017-2575-3

M3 - Article

VL - 265

SP - 143

EP - 154

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

IS - 1

ER -