Facets of the clique partitioning polytope
Mathematical Programming: Series A and B
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Identifying sets of key players in a social network
Computational & Mathematical Organization Theory
Computers and Operations Research
Detecting critical nodes in sparse graphs
Computers and Operations Research
Complexity of the critical node problem over trees
Computers and Operations Research
Most vital links and nodes in weighted networks
Operations Research Letters
On new approaches of assessing network vulnerability: hardness and approximation
IEEE/ACM Transactions on Networking (TON)
Hi-index | 0.00 |
The problem of detecting critical elements in a network involves the identification of a subset of elements (nodes, arcs, paths, cliques, etc.) whose deletion minimizes a connectivity measure over the induced network. This problem has attracted significant attention in recent years because of its applications in several fields such as telecommunications, social network analysis, and epidemic control. In this paper we examine the problem of detecting critical cliques (CCP). We first introduce a mathematical formulation for the CCP as an integer linear program. Additionally, we propose a two-stage decomposition strategy that first identifies a candidate clique partition and then uses this partition to reformulate and solve the problem as a generalized critical node problem (GCNP). To generate candidate clique partitions we test two heuristic approaches and solve the resulting (GCNP) using a commercial optimizer. We test our approach in a testbed of 13 instances ranging from 25 to 100 nodes.