Near-Optimal Distributed Tree Embedding

Tree embeddings are a powerful tool in the area of graph approximation algorithms. Essentially, they transform problems on general graphs into much easier ones on trees. Fakcharoenphol, Rao, and Talwar (FRT) [STOC’04] present a probabilistic tree embedding that transforms n-node metrics into (probability distributions over) trees, while stretching each pairwise distance by at most an O(logn) factor in expectation. This O(logn) stretch is optimal.

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