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arXiv · 1007.0489

Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs

Victor Chepoi·Feodor Dragan·Ilan Newman·Yuri Rabinovich·Yann Vaxes
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Abstract

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.

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Victor Chepoi, Feodor Dragan, Ilan Newman, Yuri Rabinovich, Yann Vaxes. 2010-07-03. Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. https://arxiv.org/abs/1007.0489

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