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6. The Shortest Common Supersequence (SCS) Given two sequences X =< X1,…,Xm > andY=, a sequence U =< u1,…,Uk > is a common supersequence of X and Y if U is a supersequence of both X and Y. The shortest common supersequence (SCS) is a common supersequence of minimal length. In the shortest common supersequence problem, the two sequences X and Y are given and the task is to find a shortest possible common supersequence of these sequences. In general, the SCS is not unique. For two input sequences, an SCS can be formed from an LCS easily. For example, if X[1..m] = abcbdab and Y[1..n]= bdcaba, the LCS is Z[1..r] = bcba. By inserting the non- Ics symbols while preserving the symbol order, we get the SCS: U[1..] = abdcabdab. The Length of the SCS is SCS_Length(X,Y) = n+m-Length_LCS(X,Y). •..

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