{"title":"RLBWT到LZ77的转换","authors":"T. Nishimoto, Yasuo Tabei","doi":"10.4230/LIPIcs.CPM.2019.9","DOIUrl":null,"url":null,"abstract":"Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler Transform (RLBWT) of a string to Lempel-Ziv 77 (LZ77) phrases of the reversed string. The first results with Policriti and Prezza's conversion algorithm [Algorithmica 2018] were $O(n \\log r)$ time and $O(r)$ working space for length of the string $n$, number of runs $r$ in the RLBWT, and number of LZ77 phrases $z$. Recent results with Kempa's conversion algorithm [SODA 2019] are $O(n / \\log n + r \\log^{9} n + z \\log^{9} n)$ time and $O(n / \\log_{\\sigma} n + r \\log^{8} n)$ working space for the alphabet size $\\sigma$ of the RLBWT. In this paper, we present a new conversion algorithm by improving Policriti and Prezza's conversion algorithm where dynamic data structures for general purpose are used. We argue that these dynamic data structures can be replaced and present new data structures for faster conversion. The time and working space of our conversion algorithm with new data structures are $O(n \\min \\{ \\log \\log n, \\sqrt{\\frac{\\log r}{\\log\\log r}} \\})$ and $O(r)$, respectively.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Conversion from RLBWT to LZ77\",\"authors\":\"T. Nishimoto, Yasuo Tabei\",\"doi\":\"10.4230/LIPIcs.CPM.2019.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler Transform (RLBWT) of a string to Lempel-Ziv 77 (LZ77) phrases of the reversed string. The first results with Policriti and Prezza's conversion algorithm [Algorithmica 2018] were $O(n \\\\log r)$ time and $O(r)$ working space for length of the string $n$, number of runs $r$ in the RLBWT, and number of LZ77 phrases $z$. Recent results with Kempa's conversion algorithm [SODA 2019] are $O(n / \\\\log n + r \\\\log^{9} n + z \\\\log^{9} n)$ time and $O(n / \\\\log_{\\\\sigma} n + r \\\\log^{8} n)$ working space for the alphabet size $\\\\sigma$ of the RLBWT. In this paper, we present a new conversion algorithm by improving Policriti and Prezza's conversion algorithm where dynamic data structures for general purpose are used. We argue that these dynamic data structures can be replaced and present new data structures for faster conversion. The time and working space of our conversion algorithm with new data structures are $O(n \\\\min \\\\{ \\\\log \\\\log n, \\\\sqrt{\\\\frac{\\\\log r}{\\\\log\\\\log r}} \\\\})$ and $O(r)$, respectively.\",\"PeriodicalId\":236737,\"journal\":{\"name\":\"Annual Symposium on Combinatorial Pattern Matching\",\"volume\":\"51 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annual Symposium on Combinatorial Pattern Matching\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.CPM.2019.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annual Symposium on Combinatorial Pattern Matching","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.CPM.2019.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
在不显式解压缩的情况下将字符串的压缩格式转换为另一种压缩格式是字符串处理的中心研究课题之一。讨论了将字符串的行长Burrows-Wheeler变换(RLBWT)转换为反向字符串的Lempel-Ziv 77 (LZ77)短语的问题。politici和Prezza的转换算法[Algorithmica 2018]的第一个结果是$O(n \log r)$时间和$O(r)$字符串长度的工作空间$n$、RLBWT中的运行次数$r$和LZ77短语的数量$z$。最近使用Kempa的转换算法[SODA 2019]的结果是$O(n / \log n + r \log^{9} n + z \log^{9} n)$时间和$O(n / \log_{\sigma} n + r \log^{8} n)$ RLBWT的字母表大小工作空间$\sigma$。在本文中,我们通过改进Policriti和Prezza的转换算法提出了一种新的转换算法,其中使用了通用的动态数据结构。我们认为这些动态数据结构可以被替换并呈现新的数据结构,以实现更快的转换。新数据结构转换算法的时间和工作空间分别为$O(n \min \{ \log \log n, \sqrt{\frac{\log r}{\log\log r}} \})$和$O(r)$。
Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler Transform (RLBWT) of a string to Lempel-Ziv 77 (LZ77) phrases of the reversed string. The first results with Policriti and Prezza's conversion algorithm [Algorithmica 2018] were $O(n \log r)$ time and $O(r)$ working space for length of the string $n$, number of runs $r$ in the RLBWT, and number of LZ77 phrases $z$. Recent results with Kempa's conversion algorithm [SODA 2019] are $O(n / \log n + r \log^{9} n + z \log^{9} n)$ time and $O(n / \log_{\sigma} n + r \log^{8} n)$ working space for the alphabet size $\sigma$ of the RLBWT. In this paper, we present a new conversion algorithm by improving Policriti and Prezza's conversion algorithm where dynamic data structures for general purpose are used. We argue that these dynamic data structures can be replaced and present new data structures for faster conversion. The time and working space of our conversion algorithm with new data structures are $O(n \min \{ \log \log n, \sqrt{\frac{\log r}{\log\log r}} \})$ and $O(r)$, respectively.