Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is...Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is defined firstly.Because it is an NP-hard combinatorial optimization problem,discrete fireworks algorithm is introduced to search the optimal solution,which is a swarm intelligence algorithm and is improved by the prior information of networks.To verify the effect of improved discrete fireworks algorithm(IDFA),experiments are carried out on various model networks and real power grid.Results show that the proposed IDFA is obviously superior to the benchmark algorithms,and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks.The key node sets found by IDFA contain a large number of non-central nodes,which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.展开更多
By a dynamical system we mean a pair of (X,T), whereX is compact Hausdorff space. In this paper we define an adherence semigroupA(X,T--X x, which is the set of all pointwise limit of subnets of(T n)n∈N. We will prove...By a dynamical system we mean a pair of (X,T), whereX is compact Hausdorff space. In this paper we define an adherence semigroupA(X,T--X x, which is the set of all pointwise limit of subnets of(T n)n∈N. We will prove some commonness between adherence semigroup and Ellis semigroup.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61502522。
文摘Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is defined firstly.Because it is an NP-hard combinatorial optimization problem,discrete fireworks algorithm is introduced to search the optimal solution,which is a swarm intelligence algorithm and is improved by the prior information of networks.To verify the effect of improved discrete fireworks algorithm(IDFA),experiments are carried out on various model networks and real power grid.Results show that the proposed IDFA is obviously superior to the benchmark algorithms,and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks.The key node sets found by IDFA contain a large number of non-central nodes,which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.
文摘By a dynamical system we mean a pair of (X,T), whereX is compact Hausdorff space. In this paper we define an adherence semigroupA(X,T--X x, which is the set of all pointwise limit of subnets of(T n)n∈N. We will prove some commonness between adherence semigroup and Ellis semigroup.
