Related papers: Counting Distinct Square Substrings in Sublinear T…
A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
An occurrence of a repeated substring $u$ in a string $S$ is called a net occurrence if extending the occurrence to the left or to the right decreases the number of occurrences to 1. The net frequency (NF) of a repeated substring $u$ in a…
In the distributed setting, the only existing constructions of \textit{sparse skeletons}, (i.e., subgraphs with $O(n)$ edges) either use randomization or large messages, or require $\Omega(D)$ time, where $D$ is the hop-diameter of the…
The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods).…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
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…
Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…
Given a string $s$ of length $n$ over a general alphabet and an integer $k$, the problem is to decide whether $s$ is a concatenation of $k$ nonempty palindromes. Two previously known solutions for this problem work in time $O(kn)$ and…
In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…
We introduce a data structure for counting pattern occurrences in texts compressed with any run-length context-free grammar. Our structure uses space proportional to the grammar size and counts the occurrences of a pattern of length $m$ in…
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
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…
Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…
We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…
The suffix array $SA[1..n]$ of a text $T$ of length $n$ is a permutation of $\{1,\ldots,n\}$ describing the lexicographical ordering of suffixes of $T$, and it is considered to be among of the most important data structures in string…
Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and…
We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given…