Looking for mathematical method/algorithm to solve described problem

[sensib0i]

Hello,

I'm looking for some mathematical method/algorithm.

I want to find the most members to form a groups.

I'll present my problem by example:

I got a set of vitamins: [A, C, D, E, K]

I got a correlation table betweeen them (synergy/antagonistic/null)



The algorithm has find best fitting groups.
* best fitting groups are these who have the most members (and the members of the groups don't duplicate / group has unique members)

Does anyone knows any algorithm or mathematical method to solve this problem?

 

[Deleted member 4993]

Hello,

I'm looking for some mathematical method/algorithm.

I want to find the most members to form a groups.

I'll present my problem by example:

I got a set of vitamins: [A, C, D, E, K]

I got a correlation table betweeen them (synergy/antagonistic/null)

View attachment 31439

The algorithm has find best fitting groups.
* best fitting groups are these who have the most members (and the members of the groups don't duplicate / group has unique members)

Does anyone knows any algorithm or mathematical method to solve this problem?

What was the topic of discussion in your class/textbook when you were given this problem?

What method/s have you been taught to solve these types of problems?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Cubist]

The algorithm has find best fitting groups.
* best fitting groups are these who have the most members (and the members of the groups don't duplicate / group has unique members)

I assume that all members must have synergy to all other members of a group? Therefore E and K could be a valid group, but A and C could not?

And what about null, could C and D be in a group together? If so, then what is the difference between null and synergy between two members?

 

[sensib0i]

What was the topic of discussion in your class/textbook when you were given this problem?

What method/s have you been taught to solve these types of problems?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

This is my personal project. I am not closed to any methods/algorithms.

I assume that all members must have synergy to all other members of a group? Therefore E and K could be a valid group, but A and C could not?

And what about null, could C and D be in a group together? If so, then what is the difference between null and synergy between two members?

Generally vitamins have synergies with each other / no interaction at all / or act agonistically.
I want to create groups based on user selected vitamins so that their number (groups) is as small as possible and as many synergies as possible are fulfilled (if there is no interaction then such vitamins can belong to a common group).


For example, by selecting 3 vitamins, [D, E, K] the algorithm should create these groups:

g1 = [E + K], size = 2
g2 = [D + K], size = 2
g3 = [E], size = 1 (because [E + D] is antagonistic)
g4 = [D], size = 1

And then arbitrarily choose the longest group (here there will be a dispute, so he can choose the first g1), check which elements belong to it and discard the considered groups which contain these vitamins (he notices that vitamin E is contained in this group, so he discards it in favour of the group g4)