Algorithms in computational geometry and graph drawing

计算几何和绘图中的算法

• 批准号: RGPIN-2015-06424
• 负责人: Lubiw, Anna
• 金额: $ 3.13万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=688590
• 关键词: Algorithms; computational; geometry; graph; drawing

My research is in design and analysis of algorithms -- specifically in the areas of computational geometry and graph algorithms. ******Graph representations are ubiquitous in computer science, engineering and the sciences -- a few examples are: road/electical/internet networks in engineering, molecular structures in chemistry, and evolutionary trees in biology. Geometry, sometimes intrinsic, and sometimes imposed, is often a valuable part of a graph representation. A big part of my work is about devising algorithms to find, manipulate and utilize such geometric representations of graphs. Specifically, one of the topics I propose working on is algorithms to represent two graphs that share some vertices and edges, with the constraint that the shared part be represented consistently. ******A current active research area is the study of algorithms to "reconfigure" geometric or combinatorial structures. "Morphing" is a popular term for some special cases of reconfiguration. I propose working on algorithms to morph between two representations of the same graph while preserving some geometric structure such as planarity. I also propose working on reconfiguration of triangulations via discrete moves called "flips". ******In a more geometric vein, my work on reconfiguration focuses on folding and flattening polyhedra. These problems have applications in manufacturing 3D shapes out of metal, cardboard or plastic. One problem is to flatten the surface of a polyhedron (e.g. imagine flattening a paper bag) continuously without using too many creases. When the surface is not flexible, Cauchy's rigidity theorem limits what can be done; we are investigating how much of the surface must be cut or made flexible to permit flattening.**

我的研究方向是算法的设计和分析--特别是在计算几何和图形算法领域。*图形表示在计算机科学、工程和科学中普遍存在--举几个例子：工程中的道路/电子/互联网网络，化学中的分子结构，以及生物学中的进化树。几何，有时是内在的，有时是强加的，通常是图形表示的一个有价值的部分。我的大部分工作是关于设计算法来发现、操作和利用这种图形的几何表示。具体地说，我建议致力于的一个主题是表示共享某些顶点和边的两个图的算法，其约束是共享部分必须一致表示。*当前一个活跃的研究领域是研究“重新配置”几何或组合结构的算法。“变形”是一个流行的术语，指的是重新配置的一些特殊情况。我建议研究算法，在保持某些几何结构(如平面性)的同时，在同一图形的两个表示之间变形。我还建议通过称为“翻转”的离散移动来重新配置三角测量。*在更几何的脉络中，我的重新配置工作重点是折叠和展平多面体。这些问题在用金属、纸板或塑料制造3D形状方面有应用。其中一个问题是在不使用太多折痕的情况下连续展平多面体的表面(例如，想象展平一个纸袋)。当表面不灵活时，柯西的刚性定理限制了可以做的事情；我们正在研究表面有多少必须被切割或变得灵活才能使其变平。