Online Embeddings

We initiate the study of on-line metric embeddings. In such an embedding we are given a sequence of n points X = x1, . . . , xn one by one, from a metric space M = (X, D). Our goal is to compute a low-distortion embedding of M into some host space, which has to be constructed in an on-line fashion, so that the image of each xi depends only on x1, . . . , xi. We prove several results translating existing embeddings to the on-line setting, for the case of embedding into p spaces, and into distributions over ultrametrics.

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Piotr Indyk, Avner Magen, Anastasios Sidiropoulos, Anastasios Zouzias
• Keywords: Algorithms, APPROX 2010, Embedding, Metric Space, On-line Metric Embeddings