Related papers: Faster Algorithms for Longest Common Substring
The longest common extension problem is to preprocess a given string of length $n$ into a data structure that uses $S(n)$ bits on top of the input and answers in $T(n)$ time the queries $\mathit{LCE}(i,j)$ computing the length of the…
A closed string $u$ is either of length one or contains a border that occurs only as a prefix and as a suffix in $u$ and nowhere else within $u$. In this paper, we present fast $\mathcal{O}(n\log n)$ time algorithms to compute all…
We show that the compressed suffix array and the compressed suffix tree of a string $T$ can be built in $O(n)$ deterministic time using $O(n\log\sigma)$ bits of space, where $n$ is the string length and $\sigma$ is the alphabet size.…
Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized…
Let $S_{T}(k)$ denote the set of distinct substrings of length $k$ in a string $T$, then the $k$-th substring complexity is defined by its cardinality $|S_{T}(k)|$. Recently, $\delta = \max \{ |S_{T}(k)| / k : k \ge 1 \}$ is shown to be a…
A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…
The \emph{longest common extension} (\emph{LCE}) problem is to preprocess a given string $w$ of length $n$ so that the length of the longest common prefix between suffixes of $w$ that start at any two given positions is answered quickly. In…
The problem of finding a longest common subsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
Let two static sequences of strings $P$ and $S$, representing prefix and suffix conditions respectively, be given as input for preprocessing. For the query, let two positive integers $k_1$ and $k_2$ be given, as well as a string $T$ given…
In this paper, we present a new data structure called the packed compact trie (packed c-trie) which stores a set $S$ of $k$ strings of total length $n$ in $n \log\sigma + O(k \log n)$ bits of space and supports fast pattern matching queries…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…
We propose algorithms that, given the input string of length $n$ over integer alphabet of size $\sigma$, construct the Burrows-Wheeler transform (BWT), the permuted longest-common-prefix (PLCP) array, and the LZ77 parsing in…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…
The Average Common Substring (ACS) is a popular alignment-free distance measure for phylogeny reconstruction. The ACS can be computed in O(n) space and time, where n=x+y is the input size. The compressed string matching is the study of…
The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes…
A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N…
The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE…