eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-06-27
5:1
5:13
10.4230/LIPIcs.CPM.2016.5
article
Faster Longest Common Extension Queries in Strings over General Alphabets
Gawrychowski, Pawel
Kociumaka, Tomasz
Rytter, Wojciech
Walen, Tomasz
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 alphabets 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 designed an algorithm with O(n log^⅔ n) running time and conjectured that O(n) time is possible. Our paper makes 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 a variant of the disjoint-sets data structure by La Poutré (SODA 1990).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol054-cpm2016/LIPIcs.CPM.2016.5/LIPIcs.CPM.2016.5.pdf
longest common extension
longest common prefix
maximal repetitions
difference cover