The first complexity and inapproximability results of the low-distortion embeddings problems between the point sets were discussed. It was proved that it is NP-hard to approximate by a ratio better than 3 the minimum distortion of a bijection between two given finite three-dimensional sets of points. Certain algorithms and hardness results for non-geometric metrics were also derived. The results propose the complexity of minimum distortion in more general settings than those solved as an important open questions.
|Number of pages||7|
|State||Published - 2005|
|Event||Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States|
Duration: 23 Jan 2005 → 25 Jan 2005
|Conference||Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms|
|Period||23/01/05 → 25/01/05|