找到最相似的字符串输入最快的方法？ [英] Fastest way to find most similar string to an input?

问题描述

由于长度为N的查询串Q，和长度的m序列的列表L确切的N，什么是最有效的算法来查找字符串L中以最少的不匹配位置至Q？例如：

Given a query string Q of length N, and a list L of M sequences of length exactly N, what is the most efficient algorithm to find the string in L with the fewest mismatch positions to Q? For example:

Q = "ABCDEFG";
L = ["ABCCEFG", "AAAAAAA", "TTAGGGT", "ZYXWVUT"];
answer = L.query(Q);  # Returns "ABCCEFG"
answer2 = L.query("AAAATAA");  #Returns "AAAAAAA".

最显而易见的方法是扫描每一个序列中L，使搜索取O（M * N）。有没有办法做到这一点在次线性时间呢？我不在乎，如果有一个大量的前期成本，组织L放入一些数据结构，因为它会被询问了很多次。此外，擅自处理追平比分是好的。

The obvious way is to scan every sequence in L, making the search take O(M * N). Is there any way to do this in sublinear time? I don't care if there's a large upfront cost to organizing L into some data structure because it will be queried a lot of times. Also, handling tied scores arbitrarily is fine.

编辑：为了澄清，我正在寻找的汉明距离

To clarify, I am looking for the Hamming distance.

推荐答案

地点敏感的哈希 underlies似乎是渐近最好的方法已知的，按照我的理解，从这个<一个href="http://mags.acm.org/communications/200801/?searchterm=nearest%2Bneighbor%2Bin%2Bhigh%2Bdimensions&pg=119"相对=nofollow>在中美洲共同市场的评论文章。说文章是pretty的毛毛，我没有读过这一切。另请参见近邻搜索。

Locality sensitive hashing underlies what seems to be the asymptotically best method known, as I understand it from this review article in CACM. Said article is pretty hairy and I didn't read it all. See also nearest neighbor search.

要涉及这些引用您的问题：他们都处理的度量空间，一组点，如n维向量空间。在您的问题，n为每个字符串的长度，并在每个坐标的值是可以出现在字符串中的每个位置的字符。

To relate these references to your problem: they all deal with a set of points in a metric space, such as an n-dimensional vector space. In your problem, n is the length of each string, and the values on each coordinate are the characters that can appear at each position in a string.

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