cases where we get VERY unbalanced groups

[kapil1garg]

This set of pairings with all student teams (except Hang since he was out) results in a group of 14-2. See if this is a bug or necessary to split.

possible reasons

• are there ways to sure the pairings aren't so "locking"?

[kapil1garg]

adding pic of the group maker's state when it occurred

[kapil1garg]

let's make a graph out of it, using this tool!

Here's the input used if anyone wants to recreate it:
Gobi
Jason
Justin
Izzy
Fardeem
Roxy
Cindy
Yvan
Molly
Issac
Parveen
Richard
Jonathan
Natalie
Harrison
Sydney
Molly Issac
Parveen Richard
Yvan Cindy
Roxy Fardeem
Jonathan Natalie
Izzy Justin
Jason
Justin Issac
Harrison Jason
Natalie Gobi
Yvan Molly
Izzy Fardeem
Sydney Cindy
Jonathan Richard

If we pair Roxy and Parveen (who were both unpaired in Pair Research), it looks like there are only 2 separate components. So, in a partition where we want 2 groups, the only possible way is to have a 14-2 split.

Removing their pairing, we now have 3 partitions of N1 = 5, N2 = 9, and N3 = 2. The most balanced partition becomes {N1, N3} (of size 7) and {N2} (of size 9).

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Within this tool itself, it's not clear what a fix would be. One approach could be to relax (by breaking) or shuffle the Pair Research pairings here seems odd, esp when there is one component that's much larger than the other.

Could also explore the Pair Research side to see in what circumstances from the Pair Research pairings would we get to a point where the graph above only has two very uneven components