Abstract
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 Bǎdoiu et al. (2007) and Bǎdoiu 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 α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K 2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.
This research was partly supported by the ANR grant BLANC GGAA.
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Chepoi, V., Dragan, F.F., Newman, I., Rabinovich, Y., Vaxès, Y. (2010). Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2010 2010. Lecture Notes in Computer Science, vol 6302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15369-3_8
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DOI: https://doi.org/10.1007/978-3-642-15369-3_8
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