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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 5, 2016

Constant Distortion Embeddings of Symmetric Diversities

  • David Bryant and Paul F. Tupper

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.

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Received: 2016-5-11
Accepted: 2016-11-8
Published Online: 2016-12-5

© 2016 David Bryant and Paul F. Tupper

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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