NSF-BSF: AF: Small: Geometric Realizations and Evolving Data

该项目涉及几何实现和不断发展的数据的综合研究。几何实现是实现组合和几何约束的关系的结构，并且演化数据捕获数据随时间变化的方式。特别感兴趣的是算法的挑战所产生的几何实现和不断发展的数据应用程序在社会中，包括物理，数据可视化，和在线服务的快速变化的数据。该项目的一个重要组成部分涉及学生参与研究;因此，该项目有可能为培养下一代信息技术研究人员带来更多的教育和研究机会。此外，美国和以色列的研究人员也将在该项目中进行合作，希望能进一步加强两国之间的联系。该项目的具体研究内容包括：* 稳定匹配Voronoi图，这是通过结合由给定点集的距离确定的几何约束和基于这些点之间的匹配偏好的组合约束确定的平面细分。*多角形，这是一个正交格中的连接细胞。这些通常用于物理学中的渗流网络模型。几何图形，是用点表示顶点，用直线表示边的图形表示。反应式数据结构，这是一种高效的数据表示，支持数据启用和禁用操作沿着查询。*近似表示，这是数据配置，为以与算法速度相称的速率变化的数据集提供良好的近似解。该研究项目的目标是在图形绘制、计算几何和计算理论的基础上，开发出快速有效的算法和数据结构。该奖项反映了NSF的法定使命，通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project involves an integrated study of geometric realizations and evolving data. Geometric realizations are structures that realize relationships combining combinatorial and geometric constraints, and evolving data captures ways in which data changes over time. Of particular interest are algorithmic challenges arising from geometric realizations and evolving data applications in society, including physics, data visualization, and on-line servicing of fast-changing data. A vital component of the project involves the involvement of students in research; hence, this project has the potential of bringing expanded educational and research opportunities for developing the next generation of information technology researchers. In addition, this project involves a collaboration between researchers in the United States and Israel, which is expected to foster further ties between these two countries.Specific topics of interest in this project include the following:* Stable-matching Voronoi diagrams, which are planar subdivisions determined by combining geometric constraints determined by distances involving a given set of points and combinatorial constraints based on matching preferences among these points.* Polyominoes, which are connected cells in an orthogonal lattice. These are often used to model percolation networks in physics.* Geometric graphs, which are representations of graphs using points for vertices and straight lines for edges.* Reactive data structures, which are efficient data representations that support data enable and disable operations along with queries.* Approximate representations, which are data configurations that provide good approximate solutions for data sets that are changing at a rate commensurate with the speed of the algorithm. For each of these and related topics, the goal of the research is to develop fast and efficient algorithms and data structures, based on exploiting methods from graph drawing, computational geometry, and theory of computation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.