当一美元变成BWT
When a Dollar Makes a BWT
摘要：
Burrows-Wheeler变换（BWT）是一种可逆的字符串变换，在文本压缩中起着核心作用，在许多现代生物信息学应用中也是基础。BWT是字符的排列，其通常具有更好的可压缩性，并且允许比原始字符串更有效地回答几种不同的查询类型。很容易看出，不是每个字符串都是BWT图像，并且BWT图像的精确特征是已知的。我们研究一个相关的组合问题。在许多应用程序中，会添加一个标记字符dollar来标记字符串的结尾，因此以dollar结尾的字符串的BWT只包含一个dollar字符。给定一个字符串w，我们询问在哪些位置（如果有的话）可以插入美元字符，以将w转换为以美元结尾的单词的BWT图像。我们表明，这只取决于标准排列的w和提出了一个O（n log n）的时间算法来识别所有这样的位置，改进的天真的二次时间算法。我们还给出了这样的位置的组合特征，并开发他们的数量和价值的界限。这是[Giuliani et al. ICTCS 2019]的扩展版本。
英文摘要：
The Burrows-Wheeler-Transform (BWT) is a reversible string transformation which plays a central role in text compression and is fundamental in many modern bioinformatics applications. The BWT is a permutation of the characters, which is in general better compressible and allows to answer several different query types more efficiently than the original string. It is easy to see that not every string is a BWT image, and exact characterizations of BWT images are known. We investigate a related combinatorial question. In many applications, a sentinel character dollar is added to mark the end of the string, and thus the BWT of a string ending with dollar contains exactly one dollar-character. Given a string w, we ask in which positions, if any, the dollar-character can be inserted to turn w into the BWT image of a word ending with dollar. We show that this depends only on the standard permutation of w and present a O(n log n)-time algorithm for identifying all such positions, improving on the naive quadratic time algorithm. We also give a combinatorial characterization of such positions and develop bounds on their number and value. This is an extended version of [Giuliani et al. ICTCS 2019].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
