Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Property testing of data dimensionality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Multi-embedding and path approximation of metric spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithm for embedding metrics into a two-dimensional space
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Correlating XML data streams using tree-edit distance embeddings
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The intrinsic dimensionality of graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On metric ramsey-type phenomena
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
XML stream processing using tree-edit distance embeddings
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the impossibility of dimension reduction in l1
Journal of the ACM (JACM)
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved embeddings of graph metrics into random trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Object Recognition as Many-to-Many Feature Matching
International Journal of Computer Vision
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Monotone maps, sphericity and bounded second eigenvalue
Journal of Combinatorial Theory Series B
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
Ramsey-type theorems for metric spaces with applications to online problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Vertex cuts, random walks, and dimension reduction in series-parallel graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Local embeddings of metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Very sparse stable random projections for dimension reduction in lα (0
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal distortion embeddings of distance regular graphs into Euclidean spaces
Journal of Combinatorial Theory Series B
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Estimators and tail bounds for dimension reduction in lα (0
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating general metric distances between a pattern and a text
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Embedding and similarity search for point sets under translation
Proceedings of the twenty-fourth annual symposium on Computational geometry
Testing embeddability between metric spaces
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Two-Dimensional Pattern Matching with Combined Scaling and Rotation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Minimum Distortion Embeddings into a Path of Bipartite Permutation and Threshold Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the internet delay space dimensionality
Proceedings of the 8th ACM SIGCOMM conference on Internet measurement
Hardness of Embedding Metric Spaces of Equal Size
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Coarse Differentiation and Multi-flows in Planar Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximated Pattern Matching with the L1 , L2 and L∞ Metrics
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Graph Augmentation via Metric Embedding
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating edit distance in near-linear time
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the geometry of graphs with a forbidden minor
Proceedings of the forty-first annual ACM symposium on Theory of computing
Randomly removing g handles at once
Proceedings of the twenty-fifth annual symposium on Computational geometry
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
New Complexity Bounds for Image Matching under Rotation and Scaling
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Unsupervised Stability-Based Ensembles to Discover Reliable Structures in Complex Bio-molecular Data
Computational Intelligence Methods for Bioinformatics and Biostatistics
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Parametric distance metric learning with label information
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Theoretical Computer Science
Randomized maps for assessing the reliability of patients clusters in DNA microarray data analyses
Artificial Intelligence in Medicine
Hardness and approximation of minimum distortion embeddings
Information Processing Letters
On the complexity of affine image matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Many-to-many matching of scale-space feature hierarchies using metric embedding
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Randomly removing g handles at once
Computational Geometry: Theory and Applications
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Lower bounds for edit distance and product metrics via Poincaré-type inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Inapproximability for planar embedding problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
New complexity bounds for image matching under rotation and scaling
Journal of Discrete Algorithms
Theoretical Computer Science
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
Many-to-many graph matching via metric embedding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
A generic framework for median graph computation based on a recursive embedding approach
Computer Vision and Image Understanding
An exact algorithm for minimum distortion embedding
Theoretical Computer Science
Subspace embeddings for the L1-norm with applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Low distortion metric embedding into constant dimension
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Limitations on quantum dimensionality reduction
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Sparser Johnson-Lindenstrauss transforms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the hardness of embeddings between two finite metrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Embedding bounded bandwidth graphs into ℓ1
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Streaming algorithms for geometric problems
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Optimal distortion embedding of complete binary trees into lines
Information Processing Letters
On approximation algorithms for data mining applications
Efficient Approximation and Online Algorithms
A sublinear-time randomized approximation scheme for the robinson-foulds metric
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Efficient two-dimensional pattern matching with scaling and rotation and higher-order interpolation
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Sparsity lower bounds for dimensionality reducing maps
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Homomorphic fingerprints under misalignments: sketching edit and shift distances
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Distortion is Fixed Parameter Tractable
ACM Transactions on Computation Theory (TOCT)
Sparser Johnson-Lindenstrauss Transforms
Journal of the ACM (JACM)
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The study of geometric representations of combinatorial structures (notably graphs) is a very wide area encompassing many disciplines. In this survey, however, we focus exclusively on geometric representations of metrics which achieve low distortion, as defined in the introduction. For a survey of many other ways of embedding combinatorial structures into geometric spaces, see [LV99].