An integer programming framework for critical elements detection in graphs
This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaini...
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| Vydané v: | Journal of combinatorial optimization Ročník 28; číslo 1; s. 233 - 273 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Boston
Springer US
01.07.2014
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| ISSN: | 1382-6905, 1573-2886 |
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| Abstract | This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework. |
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| AbstractList | This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework. |
| Author | Veremyev, Alexander Pasiliao, Eduardo L. Prokopyev, Oleg A. |
| Author_xml | – sequence: 1 givenname: Alexander surname: Veremyev fullname: Veremyev, Alexander organization: Air Force Research Laboratory, Munitions Directorate – sequence: 2 givenname: Oleg A. surname: Prokopyev fullname: Prokopyev, Oleg A. email: droleg@pitt.edu organization: Department of Industrial Engineering, University of Pittsburgh – sequence: 3 givenname: Eduardo L. surname: Pasiliao fullname: Pasiliao, Eduardo L. organization: Air Force Research Laboratory, Munitions Directorate |
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| Keywords | Critical edge detection Mixed integer programming Critical node detection Network interdiction |
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| Title | An integer programming framework for critical elements detection in graphs |
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