Computing with massive and high-dimensional data is critical to a large and diverse set of applications, including multimedia and hyperlinked databases (the World Wide Web being the prime example), data mining, machine learning, computational statistics, and vector quantization/compression. Improving performance in the above applications has been an important research goal in a variety of fields, including Computational Geometry and Databases. Unfortunately, the running times of the algorithms discovered so far depend exponentially on the dimension, which usually makes them inefficient in the aforementioned applications.   It is possible to overcome this "curse of dimensionality" and obtain algorithms that are efficient in theory and practice, as long as one is satisfied with approximate answers. From the Series:CSE Colloquia - 2000