Non-positive Curvature and the Planar Embedding Conjecture

The planar embedding conjecture asserts that any planar metric admits an embedding into L 1 with constant distortion. This is a well-known open problem with important algorithmic implications, and has received a lot of attention over the past two decades. Despite significant efforts, it has been ver...

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Bibliographic Details
Published inAnnual Symposium on Foundations of Computer Science pp. 177 - 186
Main Author Sidiropoulos, Anastasios
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.10.2013
Subjects
Computer science
Extraterrestrial measurements
Geometry
L_1
metric embeddings
multi-commodity flows
Nickel
non-positive curvature
planar embedding conjecture
planar graphs
Skeleton
sparsest cut
Upper bound
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ISSN0272-5428
DOI10.1109/FOCS.2013.27

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Summary:The planar embedding conjecture asserts that any planar metric admits an embedding into L 1 with constant distortion. This is a well-known open problem with important algorithmic implications, and has received a lot of attention over the past two decades. Despite significant efforts, it has been verified only for some very restricted cases, while the general problem remains elusive. In this paper we make progress towards resolving this conjecture. We show that every planar metric of non-positive curvature admits a constant-distortion embedding into L 1 . This confirms the planar embedding conjecture for the case of non-positively curved metrics.
ISSN:0272-5428
DOI:10.1109/FOCS.2013.27