The Art of Metric Embeddings — A technique oriented approach

During the last two decades, embeddings into finite metric spaces has emerged as an important are of research in both discrete mathematics and computer science. The powerful techniques underlying this research find numerous applications in the design and analysis of algorithms. In this survey, we try to cover the basic approach and techniques, as well as some of their applications. Unlike most surveys, we do not put as much emphasis on the results achieved in this burgeoning field. The reason is that metric embedding is such a wide domain that it seems impossible for us to present a comprehensive review in a short survey. Instead, we try to uncover the most essential ideas and techniques used in the field and relate them to similar methods used in other areas. We hope this approach would be useful to people who wish to understand why and how metric embeddings can yield so many deep and surprising results in algorithm design. This survey is in partial fulfillment of the requirements for the Ph.D. qualifying examination in computer science, HKUST The Hong Kong University of Science & Technology Ph.D Qualifying Exam Computer Science and Engineering