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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Chvátal–Sankoff constants ： ウィキペディア英語版 Chvátal–Sankoff constants In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although the existence of these constants has been proven, their exact values are unknown. They are named after Václav Chvátal and David Sankoff, who began investigating them in the mid-1970s.〔.〕〔.〕 There is one Chvátal–Sankoff constant $\backslash gamma\_k$ for each positive integer ''k'', where ''k'' is the number of characters in the alphabet from which the random strings are drawn. The sequence of these numbers grows inversely proportionally to the square root of ''k''.〔 However, some authors write "the Chvátal–Sankoff constant" to refer to $\backslash gamma\_2$, the constant defined in this way for the binary alphabet.〔.〕 ==Background== A common subsequence of two strings ''S'' and ''T'' is a string whose characters appear in the same order (not necessarily consecutively) both in ''S'' and in ''T''. The problem of computing a longest common subsequence has been well studied in computer science. It can be solved in polynomial time by dynamic programming;〔.〕 this basic algorithm has additional speedups for small alphabets (the Method of Four Russians),〔.〕 for strings with few differences,〔 for strings with few matching pairs of characters,〔.〕 etc. This problem and its generalizations to more complex forms of edit distance have important applications in areas that include bioinformatics (in the comparison of DNA and protein sequences and the reconstruction of evolutionary trees), geology (in stratigraphy), and computer science (in data comparison and revision control).〔.〕 One motivation for studying the longest common subsequences of random strings, given already by Chvátal and Sankoff, is to calibrate the computations of longest common subsequences on strings that are not random. If such a computation returns a subsequence that is significantly longer than what would be obtained at random, one might infer from this result that the match is meaningful or significant.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chvátal–Sankoff constants」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.