Approximation Algorithms for Low-Distortion Embeddings into Low-Dimensional Spaces

Mihai Bădoiu, Kedar Dhamdhere, Anupam Gupta, Yuri Rabinovich, Harald Räcke, R. Ravi and Anastasios Sidiropoulos

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. Among other results, we give an O(\sqrt{n})-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved \tilde{O}(n^{1/3}) approximation for the case of metrics generated by unweighted trees. This is the first result of this type.