The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years. 相似文献
The behaviour of masonry constructions results to be very far from the one characterizing ductile structures. In masonry constructions, the seismic action activates a rocking motion rather than a dissipating mechanism. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behaviour, until a failure condition is attained. Aim of the paper is to investigate the dynamic behaviour of masonry single storey walls, according to Housner’s studies and innovatively introducing the effect of diagonal cracks developing from the toes of the piers and shown by typical post-earthquake cracking patterns. The proposed procedure can be easily applied to the case of multi-storey regular masonry walls with openings representing the main resistant structural components of a masonry building. Starting from the evaluation of the incipient rocking acceleration of the system, the free and forced motions of the wall are examined. In the paper, according to the classical Housner’s approach, the energy dissipation occurring during the impact is modelled. Finally, a numerical application, considering a simple constant horizontal acceleration impulse of given duration has been carried out.
