Abstract: A method of expressing a target symbol sequence T relative to a reference symbol sequence R including identifying a first LCS of symbols in sequences T and R, defining the first LCS as a root node of a tree, the root node being a parent node, for each portion of the sequence T that precedes or succeeds the LCS in the sequence T, where there is a portion of the sequence R corresponding to the portion of the sequence T, identifying a subsequent LCS of symbols in the portions, if the subsequent LCS is identified, defining the subsequent LCS as a child node of the parent node, if the subsequent LCS is not identified, defining a child leaf of the parent node, and, where there is no portion of the sequence R corresponding to the portion of the sequence T, defining a child leaf of the parent node.

Abstract: A method for identifying a longest common substring for a string T and a string R, including selecting a registration symbol that appears in both strings R and T, constructing a first relative distance vector R′ from the appearance of the registration symbol in the string R, constructing a second relative distance vector T′ from the appearance of the registration symbol in the string T, deriving a substring pair RCS and TCS in the strings R and T respectively for each common substring pair RCS and TCS in the vectors R′ and T′ respectively, and identifying the longest matching of the RCS and TCS substring pairs as the longest common substring for the string T and the string R.