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We study the design of embeddings into Euclidean space with outliers.
Uniformly convex spaces
James A. Clarkson · 1936
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Distance-preserving subgraphs of hypercubes
D Ž Djoković · 1973
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Extensions of lipschitz mappings into hilbert space
William B. Johnson and Joram Lindenstrauss · 1984
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On lipschitz embedding of finite metric spaces in hilbert space
Jean Bourgain · 1985
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On isometric embeddings of graphs
Ronald L Graham and Peter M Winkler · 1985
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On scale embeddings of graphs into hypercubes
S. V. Shpectorov · 1993
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The geometry of graphs and some of its algorithmic applications
Nathan Linial, Eran London, and Yuri Rabinovich · 1994
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Recognition of the ℓ 1 \ell_{1} -graphs with complexity O ( n m ) O(nm) , or football in a hypercube
M. Deza and S. Shpectorov · 1996
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The cut cone and ℓ 1 \ell_{1} metrics
Michel Deza and Monique Laurent · 1997
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A tight bound on approximating arbitrary metrics by tree metrics
Jittat Fakcharoenphol, Satish Rao, and Kunal Talwar · 2003
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Low-distortion embeddings of finite metric spaces
Piotr Indyk and Jirí Matousek · 2004
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Metric embeddings with relaxed guarantees
I. Abraham, Y. Bartal, J. Kleinberg, T.-H.H. Chan, O. Neiman, Kedar Dhamdhere, A. Slivkins, and Anupam Gupta · 2005
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Low-distortion embeddings of general metrics into the line
Mihai Badoiu, Julia Chuzhoy, Piotr Indyk, and Anastasios Sidiropoulos · 2005
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Embedding ultrametrics into low-dimensional spaces
Mihai Badoiu, Julia Chuzhoy, Piotr Indyk, and Anastasios Sidiropoulos · 2006
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Spanners with slack
T. H. Hubert Chan, Michael Dinitz, and Anupam Gupta · 2006
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Approximation algorithms for embedding general metrics into trees
Mihai Badoiu, Piotr Indyk, and Anastasios Sidiropoulos · 2007
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Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin Farach-Colton, Mohammad Taghi Hajiaghayi, and Anastasios Sidiropoulos · 2008
Local versus global properties of metric spaces
Sanjeev Arora, László Lovász, Ilan Newman, Yuval Rabani, Yuri Rabinovich, and Santosh Vempala · 2012
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Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
Victor Chepoi, Feodor F. Dragan, Ilan Newman, Yuri Rabinovich, and Yann Vaxès · 2012
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Distortion is fixed parameter tractable
Michael R. Fellows, Fedor V. Fomin, Daniel Lokshtanov, Elena Losievskaja, Frances A. Rosamond, and Saket Saurabh · 2013
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On lipschitz extension from finite subsets
Assaf Naor and Yuval Rabani · 2015
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Reality distortion: Exact and approximate algorithms for embedding into the line
Amir Nayyeri and Benjamin Raichel · 2015
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Metric embeddings with outliers
Anastasios Sidiropoulos, Dingkang Wang, and Yusu Wang · 2015
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Inapproximability for metric embeddings into rˆd
Jirí Matousek and Anastasios Sidiropoulos · 2008
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Streaming embeddings with slack
Christiane Lammersen, Anastasios Sidiropoulos, and Christian Sohler · 2009
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Local global tradeoffs in metric embeddings
Moses Charikar, Konstantin Makarychev, and Yury Makarychev · 2010
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Fat polygonal partitions with applications to visualization and embeddings
Mark de Berg, Krzysztof Onak, and Anastasios Sidiropoulos · 2010
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Inapproximability for planar embedding problems
Jeff Edmonds, Anastasios Sidiropoulos, and Anastasios Zouzias · 2010
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A union of euclidean metric spaces is euclidean
Konstantin Makarychev and Yury Makarychev · 2016
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Approximation algorithms for low-distortion embeddings into low-dimensional spaces
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Computing bi-lipschitz outlier embeddings into the line
Karine Chubarian and Anastasios Sidiropoulos · 2020
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On l1-embeddability of unions of l1-embeddable metric spaces and of twisted unions of hypercubes
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