TY - JOUR
T1 - Minimum cost edge blocker clique problem
AU - Mahdavi Pajouh, Foad
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/11
Y1 - 2020/11
N2 - Given a graph with weights on its vertices and blocking costs on its edges, and a user-defined threshold τ> 0 , the minimum cost edge blocker clique problem (EBCP) is introduced as the problem of blocking a minimum cost subset of edges so that each clique’s weight is bounded above by τ. Clusters composed of important actors with quick communications can be effectively modeled as large-weight cliques in real-world settings such as social, communication, and biological systems. Here, we prove that EBCP is NP-hard even when τ is a fixed parameter, and propose a combinatorial lower bound for its optimal objective. A class of inequalities that are valid for the set of feasible solution to EBCP is identified, and sufficient conditions for these inequalities to induce facets are presented. Using this class of inequalities, EBCP is formulated as a linear 0–1 program including potentially exponential number of constraints. We develop the first problem-specific branch-and-cut algorithm to solve EBCP, which utilizes the aforementioned constraints in a lazy manner. We also developed the first combinatorial branch-and-bound solution approach for this problem, which aims to handle large graph instances. Finally, computational results of solving EBCP on a collection of random graphs and power-law real-world networks by using our proposed exact algorithms are also provided.
AB - Given a graph with weights on its vertices and blocking costs on its edges, and a user-defined threshold τ> 0 , the minimum cost edge blocker clique problem (EBCP) is introduced as the problem of blocking a minimum cost subset of edges so that each clique’s weight is bounded above by τ. Clusters composed of important actors with quick communications can be effectively modeled as large-weight cliques in real-world settings such as social, communication, and biological systems. Here, we prove that EBCP is NP-hard even when τ is a fixed parameter, and propose a combinatorial lower bound for its optimal objective. A class of inequalities that are valid for the set of feasible solution to EBCP is identified, and sufficient conditions for these inequalities to induce facets are presented. Using this class of inequalities, EBCP is formulated as a linear 0–1 program including potentially exponential number of constraints. We develop the first problem-specific branch-and-cut algorithm to solve EBCP, which utilizes the aforementioned constraints in a lazy manner. We also developed the first combinatorial branch-and-bound solution approach for this problem, which aims to handle large graph instances. Finally, computational results of solving EBCP on a collection of random graphs and power-law real-world networks by using our proposed exact algorithms are also provided.
KW - Edge blocker
KW - Exact algorithms
KW - Maximum weighted clique
KW - NP-hard
KW - Network interdiction
UR - http://www.scopus.com/inward/record.url?scp=85069502887&partnerID=8YFLogxK
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U2 - 10.1007/s10479-019-03315-x
DO - 10.1007/s10479-019-03315-x
M3 - Article
AN - SCOPUS:85069502887
SN - 0254-5330
VL - 294
SP - 345
EP - 376
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1-2
ER -