To extend the proposed algorithms to handle other distance measures like edit distance or normalized edit distance over the set of longest common subsequences, we would need to modify the dynamic programming tables and recurrence relations accordingly.
For edit distance, which measures the minimum number of operations (insertions, deletions, substitutions) required to transform one string into another, we can redefine the weight matrices in the DP-table to calculate the edit distance between pairs of strings. The recurrence relations would then involve updating the weights based on the specific operations needed to transform one string into another.
Similarly, for normalized edit distance, which considers the edit distance divided by the length of the strings, we would adjust the calculations in the DP-table to account for this normalization factor. The recurrence relations would need to incorporate this normalization factor in the pairwise distance calculations.
By adapting the DP-table structures and recurrence relations to accommodate the specific calculations required for edit distance or normalized edit distance, we can effectively extend the algorithms to handle these alternative distance measures over the set of longest common subsequences.