Constant Distortion Embeddings of Symmetric Diversities

David Bryant, and Paul F. Tupper. "Constant Distortion Embeddings of Symmetric Diversities." Analysis and Geometry in Metric Spaces 4.1 (2016): 326-335, electronic only. <http://eudml.org/doc/287128>.

@article{DavidBryant2016,
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.},
author = {David Bryant, Paul F. Tupper},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {diversities; metric embedding; L1 embedding; hypergraphs; symmetric diversities; embedding},
language = {eng},
number = {1},
pages = {326-335, electronic only},
title = {Constant Distortion Embeddings of Symmetric Diversities},
url = {http://eudml.org/doc/287128},
volume = {4},
year = {2016},
}

TY - JOUR
AU - David Bryant
AU - Paul F. Tupper
TI - Constant Distortion Embeddings of Symmetric Diversities
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 326
EP - 335, electronic only
AB - 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.
LA - eng
KW - diversities; metric embedding; L1 embedding; hypergraphs; symmetric diversities; embedding
UR - http://eudml.org/doc/287128
ER -