an:07203021
Zbl 1455.68045
Abedin, Paniz; Ganguly, Arnab; Hon, Wing-Kai; Matsuda, Kotaro; Nekrich, Yakov; Sadakane, Kunihiko; Shah, Rahul; Thankachan, Sharma V.
A linear-space data structure for range-LCP queries in poly-logarithmic time
EN
Theor. Comput. Sci. 822, 15-22 (2020).
00449407
2020
j
68P05 68Q25 68W32
string algorithms; longest common prefix; indexing version
In this paper, the authors study the range-LCP problem (or rlcp), which asks,
given a text \(T\) of length \(n\), for the Longest Common Prefix (LCP) of suffixes of \(T\)
(namely \(T[i,n]\) and \(T[j,n]\)) among all \(\alpha\leq i\neq j\leq \beta\),
where \(\alpha\) and \(\beta\) are integers (satisfying \(1\leq
\alpha<\beta\leq n\)) given as input.
The main question raised and positively answered by the authors is
whether it is possible to answer rlcp in polylogarithmic time, using a
linear-space data structure. More precisely, the data structure used
takes \(O(n)\) space and is constructed in \(O(n\log n)\) time. Using the
above-mentioned data structure, rlcp can then be answered in
\(O(\log^{1+\varepsilon} n)\) time, for any \(\varepsilon>0\).
Papers dealing with string algorithms are not always easy to follow
for the non-specialist, as this topic has a long and rich history, uses many
notations, and (as is the case here) aims at improving time/space
complexities and thus provides detailed and thorough analyses.
This paper is no exception. One has to be familiar with string
algorithms (and in particular with suffix arrays,
suffix trees and of course LCP issues) to understand the paper's
contents.
Guillaume Fertin (Nantes)