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- W2963952249 abstract "Abstract Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of fiite metric spaces into L1, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of L1 spaces. In the metric case, it iswell known that an n-point metric space can be embedded into L1 withO(log n) distortion. For diversities, the optimal distortion is unknown. Here, we establish the surprising result that symmetric diversities, those in which the diversity (value) assigned to a set depends only on its cardinality, can be embedded in L1 with constant distortion." @default.
- W2963952249 created "2019-07-30" @default.
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- W2963952249 date "2016-12-05" @default.
- W2963952249 modified "2023-09-24" @default.
- W2963952249 title "Constant Distortion Embeddings of Symmetric Diversities" @default.
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- W2963952249 doi "https://doi.org/10.1515/agms-2016-0016" @default.
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