Identifying sets of key players in a social network
Computational & Mathematical Organization Theory
Controlling infection by blocking nodes and links simultaneously
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Computers and Operations Research
A decomposition approach for solving critical clique detection problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
On the discovery of critical links and nodes for assessing network vulnerability
IEEE/ACM Transactions on Networking (TON)
A derandomized approximation algorithm for the critical node detection problem
Computers and Operations Research
Weighted graph-based methods for identifying the most influential actors in trust social networks
International Journal of Networking and Virtual Organisations
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In this paper we deal with the critical node problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the (weighted or unweighted) number of connections between pairs of nodes in the residual graph. In particular, we study the case where the physical network represented by graph G has a hierarchical organization, so that G is a tree. The NP@?completeness of this problem for general graphs has been already established (Arulselvan et al.). We study the subclass of CNP over trees, generalizing the objective function and constraints to take into account general nonnegative ''costs'' of node connections and ''weights'' for the nodes that are to be removed. We prove that CNP over trees is still NP@?complete when general connection costs are specified, while the cases where all connections have unit cost are solvable in polynomial time by dynamic programming approaches. For the case with nonnegative connection costs and unit node weights we propose an enumeration scheme whose time complexity is within a polynomial factor from O(1.618034^n), where n is the number of nodes of the tree. Results from computational experiments are reported for all the proposed algorithms.