eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-07
35:1
35:13
10.4230/LIPIcs.ISAAC.2017.35
article
Structural Pattern Matching - Succinctly
Ganguly, Arnab
Shah, Rahul
Thankachan, Sharma V.
Let T be a text of length n containing characters from an alphabet \Sigma, which is the union of two disjoint sets: \Sigma_s containing static characters (s-characters) and \Sigma_p containing parameterized characters (p-characters).
Each character in \Sigma_p has an associated complementary character from \Sigma_p.
A pattern P (also over \Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y.
The task is to find the starting positions (occurrences) of all such substrings S.
Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires \Theta(n\log n) bits of space, and can find all occ occurrences in time O(|P|\log \sigma+ occ), where \sigma = |\Sigma|.
In this paper, we present the first succinct index for this problem, which occupies n \log \sigma + O(n) bits and offers O(|P|\log\sigma+ occ\cdot \log n \log\sigma) query time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol092-isaac2017/LIPIcs.ISAAC.2017.35/LIPIcs.ISAAC.2017.35.pdf
Parameterized Pattern Matching
Suffix tree
Burrows-Wheeler Transform
Wavelet Tree
Fully-functional succinct tree