3 research outputs found
Faster queries for longest substring palindrome after block edit
Palindromes are important objects in strings which have been extensively
studied from combinatorial, algorithmic, and bioinformatics points of views.
Manacher [J. ACM 1975] proposed a seminal algorithm that computes the longest
substring palindromes (LSPals) of a given string in O(n) time, where n is the
length of the string. In this paper, we consider the problem of finding the
LSPal after the string is edited. We present an algorithm that uses O(n) time
and space for preprocessing, and answers the length of the LSPals in O(\ell +
\log \log n) time, after a substring in T is replaced by a string of arbitrary
length \ell. This outperforms the query algorithm proposed in our previous work
[CPM 2018] that uses O(\ell + \log n) time for each query
Efficient Representation and Counting of Antipower Factors in Words
A -antipower (for ) is a concatenation of pairwise distinct
words of the same length. The study of fragments of a word being antipowers was
initiated by Fici et al. (ICALP 2016) and first algorithms for computing such
fragments were presented by Badkobeh et al. (Inf. Process. Lett., 2018). We
address two open problems posed by Badkobeh et al. We propose efficient
algorithms for counting and reporting fragments of a word which are
-antipowers. They work in time and time, respectively, where is the number of reported fragments.
For , this improves the time complexity of
of the solution by Badkobeh et al. We also show that the
number of different -antipower factors of a word of length can be
computed in time. Our main algorithmic tools
are runs and gapped repeats. Finally we present an improved data structure that
checks, for a given fragment of a word and an integer , if the fragment is a
-antipower. This is a full and extended version of a paper from LATA 2019.
In particular, all results about counting different antipowers factors are
completely new compared with the LATA proceedings version.Comment: Full version of a paper from LATA 201
Matching Patterns with Variables
A pattern p (i.e., a string of variables and terminals) matches a word w, if
w can be obtained by uniformly replacing the variables of p by terminal words.
The respective matching problem, i.e., deciding whether or not a given pattern
matches a given word, is generally NP-complete, but can be solved in
polynomial-time for classes of patterns with restricted structure. In this
paper we overview a series of recent results related to efficient matching for
patterns with variables, as well as a series of extensions of this problem