The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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
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
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
Embedding ultrametrics into low-dimensional spaces
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
Embedding into l2∞ is easy embedding into l2∞ is NP-complete
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Improved algorithms for optimal embeddings
ACM Transactions on Algorithms (TALG)
Hardness of Embedding Metric Spaces of Equal Size
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Inapproximability for Metric Embeddings into R^d
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Geometry of Cuts and Metrics
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
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We consider the problem of computing a minimum-distortion bijection between two point-sets in R2. We prove the first non-trivial inapproximability result for this problem, for the case when the distortion is constant. More precisely, we show that there exist constants 0 3. We also apply similar ideas to the problem of computing a minimum-distortion embedding of a finite metric space into R2. We obtain an analogous inapproximability result under the l∞ norm for this problem. Inapproximability for the case of constant distortion was previously known only for dimension at least 3 [MS08].