Approximating additive distortion of embeddings into line metrics

Abstract

We consider the problem of fitting metric data on n points to a path (line) metric. Our objective is to minimize the total additive distortion of this mapping. The total additive distortion is the sum of errors in all pairwise distances in the input data. This problem has been shown to be NP-hard by [13]. We give an O(log n) approximation for this problem by using Garg et al.'s [10] algorithm for the multi-cut problem as a subroutine. Our algorithm also gives an O(log1/p n) approximation for the Lp norm of the additive distortion. © Springer-Verlag 2004.