Streaming Embeddings with Slack

We study the problem of computing low-distortion embeddings in the streaming model. We present streaming algorithms that, given an n -point metric space M , compute an embedding of M into an n -point metric space M *** that preserves a (1 *** *** )-fraction of the distances with small distortion (*** is called the slack ). Our algorithms use space polylogarithmic in n and the spread of the metric. Within such space limitations, it is impossible to store the embedding explicitly. We bypass this obstacle by computing a compact representation of M ***, without storing the actual bijection from M into M ***.