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    I would suggest that cs.stackexchange.com is a better forum for your question Commented Jan 12, 2018 at 15:19
  • Graph theory puts a lot of emphasis on the relationships between nodes. Right now I don't quite follow the topography of your collection of nodes - how are they related? If you put them on a whiteboard, what lines would you draw between them, and why? Commented Jan 12, 2018 at 15:21
  • Hi Dan, thanks for reply. I think node was wrong word to be used in context. I changed it to 'objects'. If you still think white board image will help, please let me know and I will share white board picture. I can best imagine it as if I am creating a zoo, then different animals might be compatible with certain animals. We need to keep all compatible animals in one set maximizing number of animals in zoo. And one animal cannot be repeated in any other set. I will also share pic. Thanks for your time. Commented Jan 12, 2018 at 15:52
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    I think this might be an NP-complete problem: checking whether a selection of sets is valid can be done cheaply, but to find the best combination you have to search every combination. So unless you need an exact solution, you can use a heuristic (e.g. start a search from the largest set), or use a probabilistic algorithm (e.g. a genetic algorithm). Because these are approximate, you can trade solution quality against performance. A heuristic might work very well in practice if you have more info about the structure of your problem, e.g. if you know how the sizes of sets are distributed. Commented Jan 12, 2018 at 16:01