Related papers: Lower bounds for text indexing with mismatches and…
The longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\le k$. We introduce a…
Document listing on string collections is the task of finding all documents where a pattern appears. It is regarded as the most fundamental document retrieval problem, and is useful in various applications. Many of the fastest-growing…
The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function f: U ->{0,1}^r that has specified values on the elements of a given set S, a subset of U, |S|=n, but may have…
Transformer architectures are increasingly effective at processing and generating very long chunks of texts, opening new perspectives for document-level machine translation (MT). In this work, we challenge the ability of MT systems to…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…
The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…
The impact of text length on the estimation of lexical diversity has captured the attention of the scientific community for more than a century. Numerous indices have been proposed, and many studies have been conducted to evaluate them, but…
In this work, we present a literature review for full-text and keyword indexes as well as our contributions (which are mostly practice-oriented). The first contribution is the FM-bloated index, which is a modification of the well-known…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…
We consider the approximate pattern matching problem under the edit distance. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to find the starting positions of all substrings of $T$ that can be…
We study the classic Text-to-Pattern Hamming Distances problem: given a pattern $P$ of length $m$ and a text $T$ of length $n$, both over a polynomial-size alphabet, compute the Hamming distance between $P$ and $T[i\, .\, . \, i+m-1]$ for…
In the classic longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, over an alphabet of size $\sigma$, and we are asked to find a longest string occurring as a fragment of both $S$ and…
Let $\D = $$ \{d_1,d_2,...d_D\}$ be a given set of $D$ string documents of total length $n$, our task is to index $\D$, such that the $k$ most relevant documents for an online query pattern $P$ of length $p$ can be retrieved efficiently. We…
In this paper, we study the static cell probe complexity of non-adaptive data structures that maintain a subset of $n$ points from a universe consisting of $m=n^{1+\Omega(1)}$ points. A data structure is defined to be non-adaptive when the…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…
The decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), asks to list all fragments of $T$ that are at edit distance at…
Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are…
We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…