Bounds on the Number of Longest Common Subsequences

This paper compares the standard, naive method of computing all distinct longest common subsequences, or of computing all LCS embeddings, to more efficient methods with running time comparable to the output size. Included in this analysis is a determination of the maximum possible number of LCS embeddings in two input sequences, as a function of the total number of input characters. Also included are bounds on the maximum possible number of distinct LCSs. In addition, much of the analysis carries over to cases in which the two input sequences are of the same specified length or of two independently specified lengths.