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Approximation algorithm for embedding metrics into a two-dimensional space

In this paper, we present a polynomial-time approximation algorithm for computing an embedding of an arbitrary metric into a two-dimensional space. The algorithm finds an embedding whose additive distortion is at most cε*, where ε* is the smallest additive distortion possible and c is an absolute constant. To our knowledge, this is the first result of this type, i.e., it gives an algorithm that finds (approximately) optimal embedding of a given distance matrix into a fixed d-dimensional space, where d < 1 is low, under any standard definition of embedding (see Related Work).