I'm not sure if this process has a name.

I have some words (about 9,000). They are in Japanese, but I'll try to explain this using English words. I want to categorize the words by the components (in English, letters).

A

B

C

act bar play

This should create:

A: play

B: bar

C: act

Now, 'a' appears in all 3 words, but I want to make sure that each category (letter) has at least word. Now, it would make sense to delete a word after it's used, but there are a few cases where 2 letters make up one word and that's each letter's only word--so I'd like to account for that somehow.

Is there an approach for solving this aside from brute force? Dynamic programming perhaps? Even a name for this process (if it exists) would be great.