eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-06-27
8:1
8:12
10.4230/LIPIcs.CPM.2016.8
article
Truly Subquadratic-Time Extension Queries and Periodicity Detection in Strings with Uncertainties
Iliopoulos, Costas S.
Radoszewski, Jakub
Strings with don't care symbols, also called partial words, and more general indeterminate strings are a natural representation of strings containing uncertain symbols. A considerable effort has been made to obtain efficient algorithms for pattern matching and periodicity detection in such strings. Among those, a number of algorithms have been proposed that behave well on random data, but still their worst-case running time is Theta(n^2). We present the first truly subquadratic-time solutions for a number of such problems on partial words that can also be adapted to indeterminate strings over a constant-sized alphabet. We show that $n$ longest common compatible prefix queries (which correspond to longest common extension queries in regular strings) can be answered on-line in O(n * sqrt(n * log(n)) time after O(n * sqrt(n * log(n))-time preprocessing. We also present O(n * sqrt(n * log(n))-time algorithms for computing the prefix array and two types of border array of a partial word.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol054-cpm2016/LIPIcs.CPM.2016.8/LIPIcs.CPM.2016.8.pdf
string with don’t cares
partial word
indeterminate string
longest common conservative prefix queries
prefix array