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APPROX
2010
Springer

Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs

11 years 9 months ago
Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs
We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Badoiu et al. (2007) and Badoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an -metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is . Then, for H = K2,3, we present an algorithm which either finds an -relaxed minor, or produces an O()-embedding into an outerplanar metric.
Victor Chepoi, Feodor F. Dragan, Ilan Newman, Yuri
Added 26 Oct 2010
Updated 26 Oct 2010
Type Conference
Year 2010
Where APPROX
Authors Victor Chepoi, Feodor F. Dragan, Ilan Newman, Yuri Rabinovich, Yann Vaxès
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