{"title":"更快更简单的在线/滑动最右侧 Lempel-Ziv 因式分解","authors":"Wataru Sumiyoshi, Takuya Mieno, Shunsuke Inenaga","doi":"arxiv-2408.03008","DOIUrl":null,"url":null,"abstract":"We tackle the problems of computing the rightmost variant of the Lempel-Ziv\nfactorizations in the online/sliding model. Previous best bounds for this\nproblem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for\nthe online model, and due to Larsson [CPM 2014] for the sliding model. In this\npaper, we present faster O(n log n/log log n)-time solutions to both of the\nonline/sliding models. Our algorithms are built on a simple data structure\nnamed BP-linked trees, and on a slightly improved version of the range\nminimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers.\nWe also present other applications of our algorithms.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Faster and simpler online/sliding rightmost Lempel-Ziv factorizations\",\"authors\":\"Wataru Sumiyoshi, Takuya Mieno, Shunsuke Inenaga\",\"doi\":\"arxiv-2408.03008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We tackle the problems of computing the rightmost variant of the Lempel-Ziv\\nfactorizations in the online/sliding model. Previous best bounds for this\\nproblem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for\\nthe online model, and due to Larsson [CPM 2014] for the sliding model. In this\\npaper, we present faster O(n log n/log log n)-time solutions to both of the\\nonline/sliding models. Our algorithms are built on a simple data structure\\nnamed BP-linked trees, and on a slightly improved version of the range\\nminimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers.\\nWe also present other applications of our algorithms.\",\"PeriodicalId\":501525,\"journal\":{\"name\":\"arXiv - CS - Data Structures and Algorithms\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Data Structures and Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Data Structures and Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Faster and simpler online/sliding rightmost Lempel-Ziv factorizations
We tackle the problems of computing the rightmost variant of the Lempel-Ziv
factorizations in the online/sliding model. Previous best bounds for this
problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for
the online model, and due to Larsson [CPM 2014] for the sliding model. In this
paper, we present faster O(n log n/log log n)-time solutions to both of the
online/sliding models. Our algorithms are built on a simple data structure
named BP-linked trees, and on a slightly improved version of the range
minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers.
We also present other applications of our algorithms.
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