Embedding Metric Spaces in the Rectilinear Plane: a Six-Point Criterion
نویسندگان
چکیده
We show that a metric space embeds in the rectilinear plane (i.e., is L 1-embeddable in R 2) if and only if every subspace with five or six points does. A simple construction shows that for higher dimensions k of the host rectilinear space the number c(k) of points that need to be tested grows at least quadratically with k, thus disproving a conjecture of Seth and Jerome Malitz.
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 15 شماره
صفحات -
تاریخ انتشار 1996