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The Longest Common Subsequence (LCS) problem is a very important problem inmath- ematics, which has a broad application in scheduling problems, physicsand bioinformatics. It is known that the given two random sequences of infinitelengths, the expected length of LCS will be a constant. however, the value ofthis constant is not yet known. Moreover, the variance distribution of LCSlength is also not fully understood. The problem becomes more difficult whenthere are (a) multiple sequences, (b) sequences with non-even distribution ofalphabets and (c) large alphabets. This work focus on these more complicatedissues. We have systematically analyze the expected length, variance anddistribution of LCS based on extensive Monte Carlo simulation. The results onexpected length are consistent with currently proved theoretical results, andthe analysis on variance and distribution provide further insights into theproblem.

Systematic assessment of the expected length, variance and distribution of Longest Common Subsequences