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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=614142
• 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.

我的研究是算法的设计和分析——特别是计算几何和图算法领域。 图形表示在计算机科学、工程和科学中无处不在 - 一些例子是：工程中的道路/电力/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，有时是固有的，有时是强加的，通常是图形表示的一个有价值的部分。我工作的很大一部分是设计算法来查找、操作和利用图形的几何表示。具体来说，我建议研究的主题之一是表示共享一些顶点和边的两个图的算法，并限制共享部分的表示一致。 当前活跃的研究领域是“重新配置”几何或组合结构的算法研究。 “变形”是一个流行术语，用于描述一些特殊的重新配置情况。我建议研究在同一图的两种表示之间变形的算法，同时保留一些几何结构，例如平面性。我还建议通过称为“翻转”的离散移动来重新配置三角测量。 从更几何的角度来看，我在重新配置方面的工作重点是折叠和展平多面体。这些问题可应用于用金属、纸板或塑料制造 3D 形状。一个问题是在不使用太多折痕的情况下连续压平多面体的表面（例如想象压平纸袋）。当表面不具有柔性时，柯西刚性定理会限制可以做的事情；我们正在研究必须切割多少表面或使其具有柔性才能平整。