Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Lectures on Discrete 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
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th 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
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Randomly removing g handles at once
Computational Geometry: Theory and Applications
Flow-cut gaps for integer and fractional multiflows
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Pathwidth, trees, and random embeddings
Combinatorica
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A probabilistic C-embedding of a (guest) metric M into a collection of(host) metrics M'1, ..., M'k is a randomized mapping F of M intoone of the M'1, ..., M'k such that, for any two points p,q in theguest metric: The distance between F(p) and F(q) in any M'i is not smaller thanthe original distance between p and q. The expected distance between F(p) and F(q) in (random) M'i is notgreater than some constant C times the original distance, for C≥ 1. The constant C is called the distortion of the embedding. Low-distortion probabilistic embeddings enable reducing algorithmicproblems over "hard" guest metrics into "easy" host metrics.We show that every metric induced by a graph of bounded genus can beprobabilistically embedded into planar graphs, with constant distortion. The embedding can be computed efficiently, given a drawing of the graphon a genus-g surface.