Abstract
We study the problem embedding an n-point metric space into another n-point metric space while minimizing distortion. We show that there is no polynomial time algorithm to approximate the minimum distortion within a factor of Ω((logn)1/4 − δ) for any constant δ> 0, unless \(\textnormal{NP} \subseteq \textnormal{DTIME}(n^{\textnormal{poly}(\log n))})\). We give a simple reduction from the METRIC LABELING problem which was shown to be inapproximable by Chuzhoy and Naor [10].
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Khot, S., Saket, R. (2007). Hardness of Embedding Metric Spaces of Equal Size. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_16
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DOI: https://doi.org/10.1007/978-3-540-74208-1_16
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