%0 Journal Article
%T Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
%A Victor Chepoi
%A Feodor Dragan
%A Ilan Newman
%A Yuri Rabinovich
%A Yann Vaxes
%J Mathematics
%D 2010
%I arXiv
%X In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of B\v{a}doiu, Indyk, and Sidiropoulos (2007) and B\v{a}doiu, Demaine, Hajiaghayi, Sidiropoulos, and Zadimoghaddam (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding a graph metric into an outerplanar metric. For this, we introduce a general notion of metric relaxed minor and show that if G contains an alpha-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is at meast alpha. Then, for H=K_{2,3}, we present an algorithm which either finds an alpha-relaxed minor, or produces an O(alpha)-embedding into an outerplanar metric.
%U http://arxiv.org/abs/1007.0489v1