Geometric computing

我的研究领域是计算几何，这是一个致力于设计和分析几何问题的算法和数据结构的领域。我的研究既关注理论问题，也关注实践问题。我主要研究的几何应用领域包括无线网络中的自组织路由、几何网络、网格生成/操作、图形绘制、可视化和模式识别。被证明在理论上有效的算法通常不能用于实际，因为它可能仅在问题的大小不合理地大时才变得有效，或者算法可能太复杂而无法实现。然而，理论上有效的算法的存在往往提供了对问题的见解，并导致了在实践中同样有效的算法的开发。我的研究的主要目标一直是，并将继续通过为具有理论性能保证的应用几何问题找到实用的算法解决方案，来弥合理论和实际效率之间的差距。下面，我提供了一个我目前专注于几何问题类型的例子。

My research area is Computational Geometry, a field devoted to the design and analysis of algorithms and data structures for geometric problems. My research focuses both on theoretical and practical issues. The geometric application areas I concentrate on include adhoc routing in wireless networks, geometric networks, mesh generation/manipulation, graph drawing, visualization and pattern recognition. An algorithm that is proven to be theoretically efficient often fails to be practically useful as it may only become efficient when the size of the problem is unreasonably large or the algorithm may be too complex to implement. However, the existence of theoretically efficient algorithms often provides insights into a problem and leads to the development of algorithms that are equally efficient in practice. The main goal of my research has been and continues to be to bridge the gap between theoretical and practical efficiency by finding practical algorithmic solutions to applied geometric problems that have theoretical performance guarantees. Below, I provide an example of the type of geometric problems I am currently concentrating on.