最长公共子序列的预期长度、方差和分布的系统评估
Systematic assessment of the expected length, variance and distribution of Longest Common Subsequences
摘要：
最长公共子序列问题是数学中的一个重要问题，在调度问题、物理学和生物信息学中有着广泛的应用。已知给定两个无限长随机序列，LCS的期望长度为常数。然而，这一常数的数值尚不清楚。此外，LCS长度的方差分布也没有完全理解。当存在（a）多个序列、（b）具有字母的非均匀分布的序列和（c）大字母时，问题变得更加困难。本文的工作主要集中在这些比较复杂的问题上。基于广泛的蒙特卡罗模拟，我们系统地分析了LCS的期望长度、方差和分布。期望长度的结果与目前已证明的理论结果一致，方差和分布的分析提供了进一步的见解问题。
英文摘要：
The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite lengths, the expected length of LCS will be a constant. however, the value of this constant is not yet known. Moreover, the variance distribution of LCS length is also not fully understood. The problem becomes more difficult when there are (a) multiple sequences, (b) sequences with non-even distribution of alphabets and (c) large alphabets. This work focus on these more complicated issues. We have systematically analyze the expected length, variance and distribution of LCS based on extensive Monte Carlo simulation. The results on expected length are consistent with currently proved theoretical results, and the analysis on variance and distribution provide further insights into the problem.
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