In order to investigate the cascading invulnerability attack strategy of complex network via community detection, the initial load of the node was defined by the betweenness of the node and its neighbors, this defining method comprehensively considered the information of the nodes, and the load on the broken nodes were redistributed to its neighbors according to the local preferential probability. When the network being intentionally attacked based on community detection, the couple strength, the invulnerability of Watts-Strogatz (WS) network, Barabási-Albert (BA) network, Erds-Rényi (ER) network and World-Local (WL) network, as well as network with overlapping and non-overlapping community under differet attack strategies were studied. The results show that the network's cascading invulnerability is negatively related with couple strength; as to different types of networks, under the premise that fast division algorithm correctly detects community structure, the networks invulnerability is lowest when the node with largest betweenness was attacked; after detecting overlapping community using the Clique Percolation Method (CPM), the network invulnerability is lowest when the overlapping node with largest betweenness was attacked. It comes to conclusion that the network will be largest destoryed when using the attack strategy of complex network via community detection.
A deterministic algorithm for two-stage cutting layout with same-shape block was proposed to solve the large-scale two-dimensional cutting problems. The algorithm used dynamic programming to generate the optimal same-shape block, solved the knapsack problem to determine the optimal layout of the same-shape block in the same-shape section and the same-shape section in the same-shape segment, and optimally selected the two segments to compose the optimal same-shape block layout. The algorithm was tested through 43 benchmark problems, and compared with the classic two-stage and the three-block algorithms. The experimental results indicate that the algorithm is superior in both computation time and material usage rate, it not only meets the requirements of shearing and punching process, but also achieves good results within reasonable time.
In order to investigate the effects of community structure on cascading invulnerability, in the frame of a community structure network, the initial load of the node was defined by its betweenness, and the load on the broken node was redistributed to its neighboring nodes according to the preferential probability. When the node with the largest load being intentionally attacked in the network, the relation of load exponent, coupling-strength in a community, coupling-strength between communities, modularity function and the network's invulnerability were studied. The results show that the network's cascading invulnerability is positively related with coupling-strength in a community, coupling-strength between communities and modularity function, negatively related with load exponent. With comparison to BA (Barabási-Albert) scale-free network and WS (Watts-Strogatz) small-world networks, the result indicates that community structure lowers the network's cascading invulnerability, thus the more homogeneous betweenness distribution is, the stronger network's cascading invulnerability is.