Algorithmic graph drawing

我打算继续在算法设计和分析的一般领域工作。我特别关注的是图形绘制领域，包括二维和三维的绘图。允许弯曲但面积/体积小的图纸是拟议研究的主题之一，并且在各种模型和约束下已经取得了重大进展，包括正交3D布局，约束点集，有向图等。 有效的图形绘制在需要显示大型图形结构的各种学科中至关重要-图形绘制领域的动机是这些可视化和表示问题。 在这项工作中有大量的重叠与计算几何领域和许多所需的工具是在几何背景下开发的。我对计算几何问题（例如可见性、重建和排列图）保持着浓厚的兴趣。 在过去的几年里，我的学生开发了这些领域的研究软件包和演示。我们的结果的实际应用代表了所提出的研究的一个重要方向

I intend to continue working in the general area of design and analysis of algorithms. My particular focus lies in the field of Graph Drawing, and includes drawings in both 2 and 3 dimensions. Drawings that permit bends, but with low area/volume are one theme of the proposed research, and significant progress has already been demonstrated under a variety of models and constraints, including orthogonal 3D layouts, constrained point sets, directed graphs, etc. Effective drawings of graphs are critical in various disciplines that require the display of large graphical structures -- the field of Graph Drawing is motivated by these visualization and representation problems. There is substantial overlap in this work with the field of Computational Geometry and many of the required tools were developed in geometrical contexts. I maintain a serious parallel interest in computational geometry problems such as visibility, reconstruction, and arrangement graphs. Over the past several years, software packages for research in these areas, and demos have been developed by my students. This practical application of our results represents an important direction of the proposed research