A robust model for finding optimal evolutionary trees
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Improved bandwidth approximation for trees
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Approximation algorithm for embedding metrics into a two-dimensional space
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth 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
Ordinal embeddings of minimum relaxation: general properties, trees, and ultrametrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Plane embeddings of planar graph metrics
Proceedings of the twenty-second annual symposium on Computational geometry
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Circular partitions with applications to visualization and embeddings
Proceedings of the twenty-fourth annual symposium on Computational geometry
Improved algorithms for optimal embeddings
ACM Transactions on Algorithms (TALG)
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
ACM Transactions on Algorithms (TALG)
Distortion lower bounds for line embeddings
Information Processing Letters
Minimum Distortion Embeddings into a Path of Bipartite Permutation and Threshold Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Ordinal Embedding: Approximation Algorithms and Dimensionality Reduction
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
A linear-space algorithm for distance preserving graph embedding
Computational Geometry: Theory and Applications
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hardness and approximation of minimum distortion embeddings
Information Processing Letters
Inapproximability for planar embedding problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Theoretical Computer Science
Low Distortion Maps Between Point Sets
SIAM Journal on Computing
Information Systems
An exact algorithm for minimum distortion embedding
Theoretical Computer Science
On the hardness of embeddings between two finite metrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Bandwidth and distortion revisited
Discrete Applied Mathematics
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
Optimal distortion embedding of complete binary trees into lines
Information Processing Letters
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Distortion is Fixed Parameter Tractable
ACM Transactions on Computation Theory (TOCT)
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We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. Among other results, we give an O(√n)-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative distortion. We give an improved Õ(n1/3) approximation for the case of metrics generated by unweighted trees. This is the first result of this type.