dc.citation.conferencePlace |
CN |
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dc.citation.endPage |
70 |
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dc.citation.startPage |
57 |
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dc.citation.title |
Algorithms and Data Structures Symposium (Formerly, Workshop on Algorithms and Data Structures) |
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dc.contributor.author |
Allair, Corentin |
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dc.contributor.author |
Vigneron, Antoine |
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dc.date.accessioned |
2024-01-31T21:37:42Z |
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dc.date.available |
2024-01-31T21:37:42Z |
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dc.date.created |
2021-08-02 |
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dc.date.issued |
2021-08-09 |
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dc.description.abstract |
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 log23 , this problem is NP-hard and W[1]-hard. Then we provide a near-linear time approximation algorithm for fixed k: Given an approximation ratio 0<ε⩽1 , and a positive instance of the ρ -distortion problem, our algorithm returns a solution to the (1+ε)ρ -distortion problem in time (ρ/ε)O(1)nlogn . We also show how to extend these results to the minimum distortion problem, which is an optimization version of the ρ -distortion problem where we allow scaling. For doubling spaces, we prove the same hardness results, and for fixed k, we give a (1+ε) -approximation algorithm running in time (dist(X,Y)/ε)O(1)n2logn , where dist(X,Y) denotes the minimum distortion between X and Y. |
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dc.identifier.bibliographicCitation |
Algorithms and Data Structures Symposium (Formerly, Workshop on Algorithms and Data Structures), pp.57 - 70 |
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dc.identifier.doi |
10.1007/978-3-030-83508-8_5 |
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dc.identifier.uri |
https://scholarworks.unist.ac.kr/handle/201301/77105 |
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dc.language |
영어 |
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dc.publisher |
Springer International Publishing |
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dc.title |
Pattern Matching in Doubling Spaces |
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dc.type |
Conference Paper |
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dc.date.conferenceDate |
2021-09-09 |
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