Observation matching between groups - r

Question

I am dealing with an original dataset has more than 20000 rows. A condensed version of this looks something like this below
Row x y z Group Survive
1 0.0680 0.8701 0.0619 1 78.43507
2 0.9984 0.0016 0.0000 1 89.55533
3 0.4146 0.5787 0.0068 1 85.35468
4 0.3910 0.6016 0.0074 2 67.49987
5 0.3902 0.6023 0.0075 2 81.87669
6 0.0621 0.8701 0.0678 2 27.26777
7 0.6532 0.3442 0.0026 3 53.03938
8 0.6508 0.3466 0.0026 3 62.32931
9 0.9977 0.0023 0.0000 3 97.00324
My goal is to create a column called Match1 as shown below
Row x y z Group Survive Match1
1 0.0680 0.8701 0.0619 1 78.43507 g1r1-g2r3
2 0.9984 0.0016 0.0000 1 89.55533 g1r2-g2r1
3 0.4146 0.5787 0.0068 1 85.35468 g1r3-g2r2
1 0.3910 0.6016 0.0074 2 67.49987 g1r2-g2r1
2 0.3902 0.6023 0.0075 2 81.87669 g1r3-g2r2
3 0.0621 0.8701 0.0678 2 27.26777 g1r1-g2r3
1 0.6532 0.3442 0.0026 3 53.03938 NA
2 0.6508 0.3466 0.0026 3 62.32931 NA
3 0.9977 0.0023 0.0000 3 97.00324 NA
The logic behind the values g1r1-g2r3, g1r2-g2r1, g1r3-g2r2 is as follows
1st step, a distance matrix is generated between rows in Group1 and Group2 based on Mahalanobis or simple distance method , sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
0.4235 = sqrt{ (0.3910-0.0680)^2 + (0.6016-0.8701)^2 + (0.0074-0.0619)^2}
0.4225 = sqrt{ (0.3902-0.0680)^2 + (0.6023-0.8701)^2 + (0.0075-0.0619)^2}
0.0083 = sqrt{ (0.0621-0.0680)^2 + (0.8701-0.8701)^2 + (0.0678-0.0619)^2}
0.8538 = sqrt{ (0.3910-0.9984)^2 + (0.6016-0.0016)^2 + (0.0074-0.0000)^2}
0.8549 = sqrt{ (0.3902-0.9984)^2 + (0.6023-0.0016)^2 + (0.0075-0.0000)^2}
1.2789 = sqrt{ (0.0621-0.9984)^2 + (0.8701-0.0016)^2 + (0.0678-0.0000)^2}
0.0329 = sqrt{ (0.3910-0.4146)^2 + (0.6016-0.5787)^2 + (0.0074-0.0068)^2}
Group1 vs Group2
g2r1 g2r2 g2r3
g1r1 0.4235 0.4225 0.0083
g1r2 0.8538 0.8549 1.2789
g1r3 0.0329 0.0340 0.4614
2nd step, find the minimum or smallest distance in each row.
g2r1 g2r2 g2r3
g1r1 0.4235 0.4225 **0.0083**
g1r2 **0.8538** 0.8549 1.2789
g1r3 0.0329* **0.0340** 0.4614
The column Match1 takes value g1r1-g2r3 because rows , Row1-Group1 and Row3-Group2 result in smallest distance 0.0083. Similarly g1r2-g2r1 because, Row2-Group1 and Row1-Group2 results in smallest value 0.8538. Although 0.0329 is the smallest value in the last row of the distance matrix we skip this value and chose the next smallest value 0.0340 because choosing 0.0329 will result in pairing Row3-Group1 with Row1-Group2 and Row1-Group2 is already paired with Row2-Group1, so we chose the next smallest value 0.0340 which results in g1r1-g2r3.
3rd step, calculate average survival based on matched observations in Step2.
(78.43507 - 27.26777) + (89.55533 - 67.49987) + (85.35468 -81.87669)/3 = 25.56692
I am not sure how to string together these steps programatically I would appreciate any suggestions or help putting all these pieces together efficiently.