### Abstract

Language | English |
---|---|

Pages | 2193-2200 |

Number of pages | 8 |

Journal | Computers & Operations Research |

Volume | 36 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- critical node detection
- heuristics
- integer linear programming

### Cite this

*Computers & Operations Research*,

*36*(7), 2193-2200. https://doi.org/10.1016/j.cor.2008.08.016

}

*Computers & Operations Research*, vol. 36, no. 7, pp. 2193-2200. https://doi.org/10.1016/j.cor.2008.08.016

**Detecting critical nodes in sparse graphs.** / Arulselvan, Ashwin; Commander, Clayton W.; Elefteriadou, Lily; Pardalos, Panos M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Detecting critical nodes in sparse graphs

AU - Arulselvan, Ashwin

AU - Commander, Clayton W.

AU - Elefteriadou, Lily

AU - Pardalos, Panos M.

PY - 2009/7

Y1 - 2009/7

N2 - Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the critical node problem has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is NPNP-complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

AB - Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the critical node problem has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is NPNP-complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

KW - critical node detection

KW - heuristics

KW - integer linear programming

UR - http://www.sciencedirect.com/science/article/pii/S0305054808001494

U2 - 10.1016/j.cor.2008.08.016

DO - 10.1016/j.cor.2008.08.016

M3 - Article

VL - 36

SP - 2193

EP - 2200

JO - Computers & Operations Research

T2 - Computers & Operations Research

JF - Computers & Operations Research

SN - 0305-0548

IS - 7

ER -