Pattern Matching in Doubling Spaces

@inproceedings{Allair2020PatternMI,
  title={Pattern Matching in Doubling Spaces},
  author={Corentin Allair and Antoine Vigneron},
  booktitle={Workshop on Algorithms and Data Structures},
  year={2020}
}
We consider the problem of matching a metric space (X, dX) of size k with a subspace of a metric space (Y, dY ) of size n > k, assuming that these two spaces have constant doubling dimension δ. More precisely, given an input parameter ρ > 1, the ρ-distortion problem is to find a one-to-one mapping from X to Y that distorts distances by a factor at most ρ. We first show by a reduction from k-clique that, in doubling dimension log2 3, this problem is NP-hard and W[1]hard. Then we provide a near… 
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