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

Anastasios Sidiropoulos, Mihai Badoiu, Kedar Dhamdhere, Anupam Gupta, Piotr Indyk, Yuri Rabinovich, Harald Räcke, R. Ravi

Abstract: We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the 2-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 induced by unweighted trees.