Approximating the Distortion
- Cite this paper as:
- Hall A., Papadimitriou C. (2005) Approximating the Distortion. In: Chekuri C., Jansen K., Rolim J.D.P., Trevisan L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg
Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even for 1-dimensional point sets. We also introduce additive distortion, and show that it can be easily approximated within a factor of two.
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