An optimal synchronizer for the hypercube
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
A robust model for finding optimal evolutionary trees
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Restrictions of minimum spanner problems
Information and Computation
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Tree spanners in planar graphs
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Low Stretch Spanning Trees for Planar Graphs,
Low Stretch Spanning Trees for Planar Graphs,
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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
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
Ordinal embeddings of minimum relaxation: general properties, trees, and ultrametrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fitting tree metrics: Hierarchical clustering and Phylogeny
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Metric clustering via consistent labeling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Inapproximability for planar embedding problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Theoretical Computer Science
Low Distortion Maps Between Point Sets
SIAM Journal on Computing
An exact algorithm for minimum distortion embedding
Theoretical Computer Science
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Using petal-decompositions to build a low stretch spanning tree
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Distortion is Fixed Parameter Tractable
ACM Transactions on Computation Theory (TOCT)
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We consider the problem of embedding general metrics into trees. We give the first non-trivial approximation algorithm for minimizing the multiplicative distortion. Our algorithm produces an embedding with distortion (c log n)O(√log Δ), where c is the optimal distortion, and Δ is the spread of the metric (i.e. the ratio of the diameter over the minimum distance). We give an improved O(1)-approximation algorithm for the case where the input is the shortest path metric over an unweighted graph. Moreover, we show that by composing our approximation algorithm for embedding general metrics into trees, with the approximation algorithm of [BCIS05] for embedding trees into the line, we obtain an improved approximation algorithm for embedding general metrics into the line. We also provide almost tight bounds for the relation between embedding into trees and embedding into spanning subtrees. We show that for any unweighted graph G, the ratio of the distortion required to embed G into a spanning subtree, over the distortion of an optimal tree embedding of G, is at most O(log n). We complement this bound by exhibiting a family of graphs for which the ratio is Ω(log n/log log n).