java - How to calculate minimum euclidean distance between two point sets with permutable elements? -

java - How to calculate minimum euclidean distance between two point sets with permutable elements? -

i'm working 2 sets of points have same number of elements. a0–an , b0–bn. both of these sets non-ordered. [image 1] need calculate minimum possible euclidean distance between them, taking business relationship possible permutations of elements. way know how check possible combinations of distances between 2 points, makes n! number of calculations (40320 combinations 8 points). [image 3] i've tried see if can split calculation multiple smaller calculations [image 2], haven't succeeded. there less computationally expensive way calculate it?

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java set permutation points euclidean-distance