Question

suppose there are many testcase specified by capital letter, the letters in one bracket mean these
are equal testcases. And I want the smallest set X of letters.
But there is not transitive relation for the equal testcases.
That is, （A,B） (A,D) could not get (B，D).

so,when input is:
(A,B) (A,C) (A,D) (E)
obviously the output should be (A,E) not (B,C,D,E)

when input is:
(A,B) (A,C) (A,D) (B,E) (C,F) (D,G)
in this case output should be (B,C,D) not (A,E,F.G).

when input is (A,B,C) (B,D) (C,D)
the output is either (B,C) or (A,D).

Thank you a lot.

Answer 1

This is an optimization problem that can be formulated for a branch and bound solution.
See this:
http://www.sce.carleton.ca/faculty/chinneck/po/Chapter12.pdf