Metric Embeddings and Algorithmic Applications

Low distortion embeddings of finite metric spaces is a topic at the intersection of mathematics and theoretical computer science. Much progress in this area in recent years has been motivated by algorithmic applications. Mapping complicated metrics of interest to simpler metrics (normed spaces, trees, and so on) gives access to a powerful algorithmic toolkit for approximation algorithms, online algorithms as well as for efficient search and indexing of large data sets. In a different vein, convex relaxations are a useful tool for graph partitioning problems; central to the analysis are metric embedding questions for certainly computationally defined metrics. In this course, we will see several classical and recent results on metric embeddings with a focus on algorithmic applications. Students will be expected to have a strong background in algorithms and probability.