Collaborative Research: A Formal Theory of Robust Numerical Computational Geometry and Its Validation on Configuration Space Construction

3D形状匹配、海量数据集可视化和蛋白质结构预测。理论问题涉及组合几何、算法设计和基本复杂性理论。 这项工作的目的是获得新的计算方法来解决几何或生物性质的问题，这些问题由于以下两个原因而抵制了过去的调查：要么输入数据太大，无法直接处理，只能巧妙地“采样”，要么变量的数量本身太高，以至于标准方法在运行它们所需的时间内遭受指数爆炸。需要新的降维技术来解决这个瓶颈。

3D shape matching, massive dataset visualization, and protein structure prediction. The theoretical issues involve combinatorial geometry, algorithm design and basic complexity theory. This effort is aimed at deriving new computational methods for solving problems of a geometric or biological nature that have resisted past investigations because of one two reasons: either the input data is too massive to be processed directly and it can only be "sampled" cleverly or the number of variables is itself so high that standard methods suffer from an exponential blowupin the time it takes to run them. New dimension reduction techniques are needed to resolve this bottleneck.