Efficient algorithms for inverting evolution
STOC '96 Proceedings of the twenty-eighth 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
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Low-dimensional embedding with extra information
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Virtual coordinates for ad hoc and sensor networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Theory of semidefinite programming for sensor network localization
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
Plane embeddings of planar graph metrics
Proceedings of the twenty-second annual symposium on Computational geometry
Embedding into l2∞ is easy embedding into l2∞ is NP-complete
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
ACM Transactions on Algorithms (TALG)
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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In this paper, we present a polynomial-time approximation algorithm for computing an embedding of an arbitrary metric into a two-dimensional space. The algorithm finds an embedding whose additive distortion is at most cε*, where ε* is the smallest additive distortion possible and c is an absolute constant. To our knowledge, this is the first result of this type, i.e., it gives an algorithm that finds (approximately) optimal embedding of a given distance matrix into a fixed d-dimensional space, where d any standard definition of embedding (see Related Work).