Embedding Metric
Spaces in their Intrinsic Dimension
Yair Bartal Ofer Neiman |
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Abstract A fundamental
question of metric embedding is whether he metric
dimension of a metric space is related to ts
intrinsic dimension. That is whether the dimension n which it can be embedded
in some real normed pace is implied by the
intrinsic dimension which is reflected by the inherent geometry of the space.
The existence of such an embedding was conjectured by Assouad
and was later posed as an open problem by others. This question is tightly
related to a major goal of many practical application |
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[SODA version pdf] |