Paweł Gawrychowski, T. Kociumaka, W. Rytter, Tomasz Waleń
{"title":"更快的最长公共扩展查询在一般字母的字符串","authors":"Paweł Gawrychowski, T. Kociumaka, W. Rytter, Tomasz Waleń","doi":"10.4230/LIPIcs.CPM.2016.5","DOIUrl":null,"url":null,"abstract":"Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$ LCE queries for a string of size $n$ over a general ordered alphabet can be realized in $O(q \\log \\log n+n\\log^*n)$ time making only $O(q+n)$ symbol comparisons. Consequently, all runs in a string over a general ordered alphabet can be computed in $O(n \\log \\log n)$ time making $O(n)$ symbol comparisons. Our results improve upon a solution by Kosolobov (Information Processing Letters, 2016), who gave an algorithm with $O(n \\log^{2/3} n)$ running time and conjectured that $O(n)$ time is possible. We make a significant progress towards resolving this conjecture. Our techniques extend to the case of general unordered alphabets, when the time increases to $O(q\\log n + n\\log^*n)$. The main tools are difference covers and the disjoint-sets data structure.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"92 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"31","resultStr":"{\"title\":\"Faster Longest Common Extension Queries in Strings over General Alphabets\",\"authors\":\"Paweł Gawrychowski, T. Kociumaka, W. Rytter, Tomasz Waleń\",\"doi\":\"10.4230/LIPIcs.CPM.2016.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$ LCE queries for a string of size $n$ over a general ordered alphabet can be realized in $O(q \\\\log \\\\log n+n\\\\log^*n)$ time making only $O(q+n)$ symbol comparisons. Consequently, all runs in a string over a general ordered alphabet can be computed in $O(n \\\\log \\\\log n)$ time making $O(n)$ symbol comparisons. Our results improve upon a solution by Kosolobov (Information Processing Letters, 2016), who gave an algorithm with $O(n \\\\log^{2/3} n)$ running time and conjectured that $O(n)$ time is possible. We make a significant progress towards resolving this conjecture. Our techniques extend to the case of general unordered alphabets, when the time increases to $O(q\\\\log n + n\\\\log^*n)$. The main tools are difference covers and the disjoint-sets data structure.\",\"PeriodicalId\":236737,\"journal\":{\"name\":\"Annual Symposium on Combinatorial Pattern Matching\",\"volume\":\"92 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"31\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annual Symposium on Combinatorial Pattern Matching\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.CPM.2016.5\",\"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.2016.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Faster Longest Common Extension Queries in Strings over General Alphabets
Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$ LCE queries for a string of size $n$ over a general ordered alphabet can be realized in $O(q \log \log n+n\log^*n)$ time making only $O(q+n)$ symbol comparisons. Consequently, all runs in a string over a general ordered alphabet can be computed in $O(n \log \log n)$ time making $O(n)$ symbol comparisons. Our results improve upon a solution by Kosolobov (Information Processing Letters, 2016), who gave an algorithm with $O(n \log^{2/3} n)$ running time and conjectured that $O(n)$ time is possible. We make a significant progress towards resolving this conjecture. Our techniques extend to the case of general unordered alphabets, when the time increases to $O(q\log n + n\log^*n)$. The main tools are difference covers and the disjoint-sets data structure.