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Find the bijection that preserves distances best

I have two spaces (not necessarily equal in dimension) with N points. I try to find a bijection (pairing) of points, so that the distances are preserved as best as possible.

It seems that I can not find a discussion of possible solutions or algorithms for this issue on the Internet. Can anyone suggest keywords that I could search for? Does this problem have a name or does it appear in any domain?

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I believe that you are looking for a multidimensional scaling algorithm in which you minimize the overall change in distance. Unfortunately, I have very little experience in this area and could not be more useful.

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I have not heard about the same problem. There are two similar types of problems:

  • A non-linear decrease in dimension, you are given N points with large sizes, and you want to find N low-dimensional points that preserve distance, as well as possible. MDS, mentioned by Michael Kowal, is one such method.
  • : . , Kuhn-Munkres ( ), NxN, pi pj, . , , b- (Kuhn-Munkres 1-).

, " ", , (2), (2) , , .

, Kuhn-Munkres .

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