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- W2000262490 abstract "We prove that every tree T=(V, E) on n vertices can be embedded in the plane with distortion $$ O(sqrt n )$$ that is, we construct a mapping f: V → R 2 such that $$ rho (u,upsilon ) leqslant parallel f(u) - f(upsilon )parallel leqslant O(sqrt n ) cdot rho (u,upsilon )$$ for every u, υ ∈ V, where ρ(u, υ) denotes the length of the path from u to υ in T (the edges have unit lengths).The embedding is described by a simple and easily computable formula.This is asymptotically optimal in the worst case. We also prove several related results." @default.
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- W2000262490 date "2002-01-01" @default.
- W2000262490 modified "2023-09-27" @default.
- W2000262490 title "Low-Distortion Embeddings of Trees" @default.
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- W2000262490 doi "https://doi.org/10.1007/3-540-45848-4_27" @default.
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