The Shortest Common Supersequence Problem over Binary Alphabet is NP-Complete

@article{Rih1981TheSC,
  title={The Shortest Common Supersequence Problem over Binary Alphabet is NP-Complete},
  author={Kari-Jouko R{\"a}ih{\"a} and Esko Ukkonen},
  journal={Theor. Comput. Sci.},
  year={1981},
  volume={16},
  pages={187-198}
}
We consider the complexity of the Shortest Common Supersequence (SCS) problem, i.e. the problem of finding for finite strings S1, $2, . . . , S,, a shortest string S such that every Si can be obtained 3y deleting zero or more elements from S. The SCS problem is shown to be NP-complete fur strings over an alphabet of size 22. Given a string S over an alpha.bet 2, we define a sapersequerzce S’ of S to be any string S’ = Wo~1~1~2~2 l l l xkwk over C such that S =. x1x2 9 l .xck and each wi E X*. A… CONTINUE READING

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