A vertex incremental approach for maintaining chordality

For a chordal graph G=(V,E), we study the problem of whether a new vertex u∉V and a given set of edges between u and vertices in V can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, specify a maximal subset of the proposed edges that can be added along with u, or conversely, a minimal set of extra edges that can be added in addition to the given set, so that the resulting graph is chordal. In order to do this, we give a new characterization of chordal graphs and, for each potential new edge uv, a characterization of the set of edges incident to u that also must be added to G along with uv. We propose a data structure that can compute and add each such set in O(n) time. Based on these results, we present an algorithm that computes both a minimal triangulation and a maximal chordal subgraph of an arbitrary input graph in O(nm) time, using a totally new vertex incremental approach. In contrast to previous algorithms, our process is on-line in that each new vertex is added without reconsidering any choice made at previous steps, and without requiring any knowledge of the vertices that might be added subsequently.     

Generating even triangulations of the projective plane

We shall determine the 20 families of irreducible even triangulations of the projective plane. Every even triangulation of the projective plane can be obtained from one of them by a sequence of even‐splittings and attaching octahedra, both of which were first given by Batagelj 2 . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 333–349, 2007     

Triangulations in CGAL

This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library .     

二元样条的积分表示及分层三角剖分下二次样条空间的维数

本文通过引入一个积分协调条件，首次给出了二元样条的一个积分表示．文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数．     

EPR‐Based Approach for the Localization of Paramagnetic Metal Ions in Biomolecules

Metal ions play an important role in the catalysis and folding of proteins and oligonucleotides. Their localization within the three‐dimensional fold of such biomolecules is therefore an important goal in understanding structure–function relationships. A trilateration approach for the localization of metal ions by means of long‐range distance measurements based on electron paramagnetic resonance (EPR) is introduced. The approach is tested on the Cu²⁺ center of azurin, and factors affecting the precision of the method are discussed.     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

基于Delaunay三角剖分的地表平均温度模拟

利用Delaunay三角网对目标区域进行剖分,在对地表温度进行高度插值后,运用二重积分的思想建立了基于Delaunayr三角剖分的地表平均温度测量模型.同时以南极地表平均温度的测量为例,将67个自动气象地表台站、46个气象地表台站以及56个高空气象观测站的加权平均温度与地表平均温度的数据进行分析,得到南极2015全年地表平均温度均在-8℃以下,最低温约为-20℃,符合南极大陆地表温度的实际情况.     

An efficient adaptive analysis procedure for node-based smoothed point interpolation method (NS-PIM)

This paper presents an efficient adaptive analysis procedure being able to operate in the framework of the node-based smoothed point interpolation method (NS-PIM). The NS-PIM uses three-node triangular cells and is very easy to be implemented, which make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a new error indicator is devised for NS-PIM settings; two ways are proposed to calculate the local critical value; a simple h-type local refinement scheme is adopted and Delaunay technology is used for regenerating optimal new mesh. A number of typical numerical examples involving stress concentration and solution singularities have been tested. The results demonstrate that the present procedure achieves much higher convergence rate results compared to the uniform refinement, and can obtain upper bound solution in strain energy.     

Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin [10] proved that the second conjecture is true for all planar triangulations. First, we construct for each p ≥ 1, a biconnected outerplanar graph of pathwidth 2p + 1 whose (geometric) dual has pathwidth p + 1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin [3], implied by one of Fomin [10]. Finally we prove, in an algorithmic way, that the pathwidth of every biconnected outerplanar graph is at most twice the pathwidth of its (geometric) dual minus one. A tight interval for the studied relation is therefore obtained, and we show that all cases in the interval happen. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 27–41, 2007     

Bivariate quartic spline spaces and quasi-interpolation operators

In this paper, we study two bivariate quartic spline spaces and , and present two classes of quasi-interpolation operators in the two spaces, respectively. Some results on the operators are given.