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!