Hello,
given the following data pairs:
A-B
A-C
A-D
A-E
A-F
B-C
B-D
B-E
B-F
C-D
C-E
C-F
D-E
D-F
E-F
with n = 6 being the number of unique single entities. I want to calculate one possible solution for the highest possible parallelisation.
Assuming each element can only exist once at a certain time, I can determine the maximum number of parallel slots as
.
I would like to find a possible valid arrangement of the data pairs.
One possible valid (every element is only allowed once per row) solution might look like this:
I thought about randomly filling each row with the "left over" data-pairs starting with row 1 and checking their validity, however starting with row 3 you quickly run into solutions where not all columns can be filled out e.g.
Can anyone give me a hint of how to best approach this topic?
Thanks a lot!
given the following data pairs:
A-B
A-C
A-D
A-E
A-F
B-C
B-D
B-E
B-F
C-D
C-E
C-F
D-E
D-F
E-F
with n = 6 being the number of unique single entities. I want to calculate one possible solution for the highest possible parallelisation.
Assuming each element can only exist once at a certain time, I can determine the maximum number of parallel slots as
Excel Formula:
=ROUNDDOWN(n/2,0)
I would like to find a possible valid arrangement of the data pairs.
One possible valid (every element is only allowed once per row) solution might look like this:
B - C | D - F | A - E |
C - E | A - D | B - F |
A - B | D - E | C - F |
A - C | B - D | E - F |
A - F | B - E | C - D |
I thought about randomly filling each row with the "left over" data-pairs starting with row 1 and checking their validity, however starting with row 3 you quickly run into solutions where not all columns can be filled out e.g.
B - C | D - F | A - E |
C - E | A - D | B - F |
A - B | C - D | E - F |
A - C | B - D | |
A - F | D - E | |
B - E | C - F |
Can anyone give me a hint of how to best approach this topic?
Thanks a lot!