Demystifying the Computer SciencePhD Admission in US Universities, Part I
8/22/2023Low distortion metric embeddings provide a powerful algorithmic toolkit, with applications ranging from approximation/sublinear/online/distributed algorithms, to machine learning , biology, and computer vision. We say that an embedding $f$ from a metric space $(X,d_X)$ to a metric space $(Y,d_Y)$ has multiplicative distortion $t$, if the embedding is dominating for every pair of points $u,v\in X$ it holds that $\alpha\cdot d_X(u,v)\le d_Y(f(u),f(v))\le t\cdot \beta\cdot d_X(u,v)$ for some constans $\alpha,\beta$. Typical applications of metric embeddings have the following structure: take some instance of a problem in a "hard" metric space $(X,d_X)$; embed $X$ into a "simple" metric space $(Y,d_Y)$ via a low-distortion metric embedding $f$; solve the problem in $Y$, and "pull-back" the solution to $X$. Thus, the objectives are low distortion and "simple" target space. The two notable metric embedding workshops, one organized in Haifa, Israel in 2002 and another organized in Princeton in 2003, have been very successful till this day: they introduced metric embedding to the broader theory community and provided a host of open problems that have served as an excellent guidance for advancing the field much further. Over the last two decades, significant progress has been made on many open problem put forth by the 2002-2003 workshops At the same time, many new research directions in metric embedding have emerged. Here we highlight several examples. These developments have lead to new algorithm design techniques as well as a deeper understanding of a variety of metric spaces. On the other hand, they opened up a host of challenging problems. The goal of our workshop is to bring the forefronts in the area of metric embeddings to the broader theory community. By doing so, we hope that researchers in different areas could exploit the new ideas and techniques in metric embedding developed over the past two decades to solve their problems. Organizers Arnold Filtser (Bar-Ilan University)
2/23/2023or
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