Algorithmic Applications of Low-Distortion Geometric Embeddings

The author surveys algorithmic results obtained using low-distortion embeddings of metric spaces into (mostly) normed spaces. He shows that low-distortion embeddings provide a powerful and versatile toolkit for solving algorithmic problems. Their fundamental nature makes them applicable in a variety of diverse settings, while their relation to rich mathematical fields (e.g., functional analysis) ensures availability of tools for their construction.

The dimension of almostspherical sections of…The dimension of almost spherical sections of convex bodiesOn lipschitz embeddingof finite metric spaces…On lipschitz embedding of finite metric spaces in Hilbert spaceThe Geometry of Graphsand Some of its…The Geometry of Graphs and Some of its Algorithmic ApplicationsProbabilisticApproximations of Metri…Probabilistic Approximations of Metric Spaces and Its Algorithmic ApplicationsOn ApproximatingArbitrary Metrices by…On Approximating Arbitrary Metrices by Tree MetricsApproximating a FiniteMetric by a Small Numbe…Approximating a Finite Metric by a Small Number of Tree MetricsLower Bounds on theDistortion of Embedding…Lower Bounds on the Distortion of Embedding Finite Metric Spaces in GraphsSmall Distortion andVolume Preserving…Small Distortion and Volume Preserving Embeddings for Planar and Euclidean MetricsCuts, Trees andl1-Embeddings of GraphsCuts, Trees and l1-Embeddings of GraphsAn Algorithmic Theory ofLearning: Robust…An Algorithmic Theory of Learning: Robust Concepts and Random ProjectionApproximating theBandwidth via Volume…Approximating the Bandwidth via Volume Respecting EmbeddingsLectures on discretegeometryLectures on discrete geometryFinite metric spaces:combinatorics, geometry…Finite metric spaces: combinatorics, geometry and algorithmsLow Stretch SpanningTreesLow Stretch Spanning TreesGraph DecompositionLemmas and Their Role i…Graph Decomposition Lemmas and Their Role in Metric Embedding MethodsApproximating EditDistance EfficientlyApproximating Edit Distance EfficientlyLow-distortionembeddings of general…Low-distortion embeddings of general metrics into the lineThe complexity oflow-distortion…The complexity of low-distortion embeddings between point setsRamsey-type theorems formetric spaces with…Ramsey-type theorems for metric spaces with applications to online problemsEmbedding Metrics intoUltrametrics and Graphs…Embedding Metrics into Ultrametrics and Graphs into Spanning Trees with Constant Average DistortionA novel approach toembedding of metric…A novel approach to embedding of metric spaces (גישה חדשה לשיכונים של מרחבים מטריים.)On the geometry ofgraphs with a forbidden…On the geometry of graphs with a forbidden minorGeometric ApproximationAlgorithmsGeometric Approximation AlgorithmsClan Embeddings intoTrees, and Low Treewidt…Clan Embeddings into Trees, and Low Treewidth GraphsAlgorithmic Applicationsof Low-Distortion…Algorithmic Applications of Low-Distortion Geometric EmbeddingsEarlier referencesFocus paperCiting papersOlderNewer

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