Detecting critical nodes in sparse graphs

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 p...

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Bibliographic Details
Published in:Computers & operations research 2009-07, Vol.36 (7), p.2193-2200
Main Authors: Arulselvan, Ashwin, Commander, Clayton W., Elefteriadou, Lily, Pardalos, Panos M.
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorial optimization
Critical node detection
Exact sciences and technology
Flows in networks. Combinatorial problems
Graph theory
Heuristic
Heuristics
Integer linear programming
Integer programming
Linear programming
Mathematical programming
NP-complete
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Studies
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Summary: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 NP -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.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2008.08.016