图的圈和路剖分问题

设G是一个顶点数为n的图，k为任意正整数且k≤n，证明了如果图G中任何一对不相邻顶点的最大度至少为n-k＋1/2，则G能剖分成k个子图Hi,1≤i≤k，其中Hi是圈或路；如果G是2-连通图，σ2（G）=min{dG（x）＋dG（y）x，Y∈y（G），x≠y，d（x，y）=2}≥n-k，G也能剖分成k个子图Hi，1≤i≤k，其中Hi是圈或路。     

A spatial cognition-based urban building clustering approach and its applications

This article presents a spatial cognition analysis technique for automated urban building clustering based on urban morphology and Gestalt theory. The proximity graph is selected to present the urban mrphology. The proximity graph considers the local adjacency among buildings, providing a large degree of freedom in object displacement and aggregation. Then, three principles of Gestalt theories, proximity, similarity, and common directions, are considered to extract potential Gestalt building clusters. Next, the Gestalt features are further characterized with seven indicators, that is, area difference, height difference, similarity difference, orientation difference, linear arrangement difference, interval difference, and oblique degree of arrangement. A support vector machine (SVM)-based approach is employed to extract the Gestalt building clusters. This approach transforms the Gestalt cluster extraction into a supervised discrimination process. The method presents a generalized approach for clustering buildings of a given street block into groups, while maintaining the spatial pattern and adjacency of buildings during the displacement operation. In applications of urban building generalization and three-dimensional (3D) urban panoramic-like view, the method presented in this article adequately preserves the spatial patterns, distributions, and arrangements of urban buildings. Moreover, the final 3D panoramic-like views ensure the accurate appearance of important features and landscapes.     

基于子图运算的空间数据拓扑关系及其自动生成

讨论了地图的基本元素及其拓扑关系．采用先建立子图拓扑关系，再以并运算方式产生图拓扑关系的思想。在实现方式上，以栅格影像为基础，用种子填充方式产生子图拓扑关系；采用面目标匹配法顺序搜索方式合并子图，生成图拓扑关系，并以自动方式实现上述思想．