The Critical node Problem (CNP) aims to identify k nodes from an undirected graph G=(V,E), in order to minimize the number of pairwise connected nodes in the residual graph after deleting these k nodes. This problem h...
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ISBN:
(纸本)9781538660058
The Critical node Problem (CNP) aims to identify k nodes from an undirected graph G=(V,E), in order to minimize the number of pairwise connected nodes in the residual graph after deleting these k nodes. This problem has a wide range of applications in the fields of cyber security, disease control, biological analysis, social network, etc. The CNP is known to be NP-hard, and heuristics are commonly used to solve large-scale CNP instances, among which the node-exchange operation is a basic move operator widely adopted by local-search based heuristics. Given an initial CNP solution consisting of k nodes, there are totally kx (vertical bar V vertical bar-k) possible node-exchange operations. The current best algorithm requires a complexity of O((vertical bar V vertical bar-k)x(vertical bar V vertical bar+vertical bar E vertical bar+kxD(G))) to evaluate all these operations (vertical bar V vertical bar denotes the number of nodes, vertical bar E vertical bar denotes the number of edges, D(G) denotes the maximum degree of the node in graph G),In this paper, a series of dynamic data structures are implemented to reduce the above complexity to O((vertical bar V vertical bar-k)x(vertical bar V vertical bar+vertical bar E vertical bar)), so as to improve the efficiency of local search.
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