Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
A polylog(n)-competitive algorithm for metrical task systems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Approximating the bandwidth via volume respecting embeddings (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A polynomial time approximation scheme for minimum routing cost spanning trees
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Girth and euclidean distortion
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A lower bound on the distortion of embedding planar metrics into Euclidean space
Proceedings of the eighteenth annual symposium on Computational geometry
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
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
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A tight upper bound on the probabilistic embedding of series-parallel graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Randomly removing g handles at once
Proceedings of the twenty-fifth annual symposium on Computational geometry
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
Bilipschitz snowflakes and metrics of negative type
Proceedings of the forty-second ACM symposium on Theory of 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
A simpler algorithm and shorter proof for the graph minor decomposition
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Embedding bounded bandwidth graphs into ℓ1
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Bandwidth and low dimensional embedding
Theoretical Computer Science
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Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into \math space. The main results are: 1. Explicit constant-distortion embeddings of all series-parallel graphs, and all graphs with bounded Euler number. These are thus the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, we obtain algorithms to approximate the sparsest cut in such graphs to within a constant factor. 2. A constant-distortion embedding of outerplanar graphs into the restricted class of \math-metrics known as "dominating tree metrics". We also show a lower bound of \math on the distortion for embeddings of series-parallel graphs into (distributions over) dominating tree metrics. This shows, surprisingly, that such metrics approximate distances very poorly even for families of graphs with low treewidth, and excludes the possibility of using them to explore the finer structure of \math-embeddability.