On the recognition of permuted Supnick and incomplete Monge matrices

Incomplete Monge matrices are a generalization of standard Monge matrices: the values of some entries are not specified and the Monge property only must hold for all specified entries. We derive several combinatorial properties of incomplete Monge matrices and prove that the problem of recognizingpermuted incomplete Monge matrices is NP-complete. For the special case of permutedSupnick matrices, we derive a fast recognition algorithm and thereby identify a special case of then-vertex travelling salesman problem which can be solved inO(n ²logn) time.     

Spanning trees and shortest paths in monge graphs

We investigate three problems onMonge graphs, i.e. complete, undirected weighted graphs whose distance matrix is a Monge matrix: (A) the minimum spanning tree problem, (B) the problem of computing all-pairs shortest paths and (C) the problem of determining a minimum weighted 1-to-all shortest path tree. For all three problems best possible algorithms (in terms of complexity) are presented. This research has been supported by the Spezialforschungsbereich F 003 ‘Optimierung und Kontrolle’/Projektbereich Diskrete Optimierung.     

基于包含原理一般动态互联系统的分解与分散控制

针对一般结构互联系统的动态变化, 通过系统结构的描述, 以包含原理的多重叠分解为基础, 构建出适用于一般结构互联系统对对分解与重叠分散控制的扩展收缩变换矩阵、置换矩阵及相关的补偿矩阵; 然后根据所提出的子系统对的删除与添加方式, 构建出相应的删除矩阵与添加矩阵, 并将两者结合得到用于完成结构变化后的互联系统对对分解与重叠分散控制的结构变化矩阵, 从而实现具有一般动态结构互联系统的分解与分散控制; 最后以四区域互联电力系统AGC为例对其进行详细说明.

     

Monge mapping using hierarchical NURBS

Texture mapping is an efficient and effective tool in computer graphics and animation. While computationally very cost-effective, texture mapping may produce non-realistic appearances of shapes in 3D environment, especially when viewing closely. To improve the realism of 3D modeling, bump mapping technique is developed to add details with the 3D models on top of texture mapping. Bump mapping, however, offers only simple and visual enhancement. Displacement mapping technique can further improve the localized detail of geometry. In this paper, Monge mapping technique is developed for detail and local shape modification of NURBS represented geometry in a 3D environment. Based on multiresolution and refinement schemes, Hierarchical NURBS (H-NURBS) is first investigated to design a mechanism for the purpose of carrying localized geometric information. Monge mapping on H-NURBS patch can be easily performed via simple cut-and-paste operation. Parametric control of the local shapes is developed to facilitate easier and better 3D local modeling.