论文信息 - The Euclidean Distortion of Complete Binary Trees

The Euclidean Distortion of Complete Binary Trees

Abstract. Bourgain [1] showed that every embedding of the complete binary tree of depth n into l2 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.

Michael E. Saks | Nathan Linial

[1] J. Bourgain. On lipschitz embedding of finite metric spaces in Hilbert space , 1985 .

[2] J. M. Sek. On embedding trees into uniformly convex Banach spaces , 1999 .