Abstract. Bourgain [1] showed that every embedding of the complete binary tree of depth n into l 2 has metric distortion ≥
$\Omega(\sqrt{\log n})$
. An alternative proof was later given by Matousek [3]. This note contains a short proof for this fact.
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Linial, ., Saks, . The Euclidean Distortion of Complete Binary Trees . Discrete Comput Geom 29, 19–21 (2002). https://doi.org/10.1007/s00454-002-2827-z
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DOI: https://doi.org/10.1007/s00454-002-2827-z