We present two metaheuristics for the Critical Node Problem, that is, the maximal fragmentation of a graph through the deletion of nodes. The two metaheuristics are based on the Iterated Local Search and Variable Neighborhood Search frameworks. Their main characteristic is to exploit two smart and computationally efficient neighborhoods which we show can be implemented far more efficiently than the classical neighborhood based on the exchange of any two nodes in the graph, and which we prove is equivalent to the classical neighborhood in the sense that it yields the same set of neighbors. Solutions to improve the overall running time without deteriorating the quality of the solution computed are also illustrated. The results of the proposed metaheuristics outperform those currently available in literature. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 209–221 2016

Abstract Peer‐to‐peer (P2P) applications are rapidly gaining acceptance among users of Internet‐based services, especially because of their capability of exchanging resources while preserving the anonymity of both requesters and providers. However, concerns have been raised about the possibility that malicious users can exploit the network to spread tampered‐with resources (e.g., malicious programs and viruses). A considerable amount of research has thus focused on the development of trust and reputation models in P2P networks. In this article, we propose to use fuzzy techniques in the design of reputation systems based on collecting and aggregating peers' opinions. Fuzzy techniques are used in the evaluation and synthesis of all the opinions expressed by peers. The behavior of the proposed system is described by comparison with probabilistic approaches.