Editing Longest common subsequence (section)

== Relation to other problems ==
For two strings <math>X_{1 \dots m}</math> and <math>Y_{1 \dots n}</math>, the length of the [[shortest common supersequence problem|shortest common supersequence]] is related to the length of the LCS by<ref name="BHR00" />

:<math>\left|SCS(X,Y)\right| = n + m - \left|LCS(X,Y)\right|.</math>

The [[edit distance]] when only insertion and deletion is allowed (no substitution), or when the cost of the substitution is the double of the cost of an insertion or  deletion, is:

:<math>d'(X,Y) = n + m - 2 \cdot \left|LCS(X,Y)\right|.</math>