Related papers: Efficient Algorithms to Compute Closed Substrings
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…
Many problems in Computer Science can be abstracted to the following question: given a set of objects and rules respectively, which new objects can be produced? In the paper, we consider a succinct version of the question: given a set of…
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…
The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given…
Let $w$ be a string of length $n$. The problem of counting factors crossing a position - Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Leqroc, and Rytter, 2021], asks to count the number $\mathcal{C}(w,k)$…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) $n$-input Subset Sum problem that runs in time $2^{(1/2 - c)n}$ for some constant $c>0$. In this paper we give a Subset Sum algorithm with…
This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…
We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…
We have rediscovered a simple algorithm to compute the mathematical constant \[ \pi=3.14159265\cdots. \] The algorithm had been known for a long time but it might not be recognized as a fast, practical algorithm. The time complexity of it…
In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…
Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$…
Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…
We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of $d$ strings of length $m$ and an integer $k$, we must preprocess it into a data structure to answer the following queries: Given a query…
We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of…
In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the \emph{minimum spanning tree (MST)} problem in the \emph{Congested Clique} model was first improved to $O(\log \log \log n)$ from…
Given \(k\) strings each of length at most $n$, computing the shortest common supersequence of them is a well-known NP-hard problem (when \(k\) is unbounded). On the other hand, when \(k=2\), such a shortest common supersequence can be…
We show that the number of distinct squares in a packed string of length $n$ over an alphabet of size $\sigma$ can be computed in $O(n/\log_\sigma n)$ time in the word-RAM model. This paper is the first to introduce a sublinear-time…