Related papers: Efficiently Approximating Edit Distance Between Ps…
Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space…
We consider an \emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\in\{0,1\}^n$ from $m$ traces (each trace is generated independently by passing $s$ through a probabilistic…
Quasiperiodicity in strings was introduced almost 30 years ago as an extension of string periodicity. The basic notions of quasiperiodicity are cover and seed. A cover of a text $T$ is a string whose occurrences in $T$ cover all positions…
In the problem of the longest common substring with $k$ mismatches we are given two strings $X, Y$ and must find the maximal length $\ell$ such that there is a length-$\ell$ substring of $X$ and a length-$\ell$ substring of $Y$ that differ…
Pairwise sequence comparison is one of the most fundamental problems in string processing. The most common metric to quantify the similarity between sequences S and T is edit distance, d(S,T), which corresponds to the number of characters…
We study the problem of computing similarity joins under edit distance on a set of strings. Edit similarity joins is a fundamental problem in databases, data mining and bioinformatics. It finds important applications in data cleaning and…
In this paper we provide a new locally consistent decomposition of strings. Each string $x$ is decomposed into blocks that can be described by grammars of size $\widetilde{O}(k)$ (using some amount of randomness). If we take two strings $x$…
The Swap-Insert Correction distance from a string $S$ of length $n$ to another string $L$ of length $m\geq n$ on the alphabet $[1..d]$ is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting $S$ into $L$.…
Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…
The Dyck language, which consists of well-balanced sequences of parentheses, is one of the most fundamental context-free languages. The Dyck edit distance quantifies the number of edits (character insertions, deletions, and substitutions)…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. For example, edit distance of two strings of length $n$ can be solved in $O(n^2/w)$ time. In a reasonable…
The Earth Mover's Distance (EMD) is a state-of-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation…
Given a hereditary property of graphs $\mathcal{H}$ and a $p\in [0,1]$, the edit distance function ${\rm ed}_{\mathcal{H}}(p)$ is asymptotically the maximum proportion of edge-additions plus edge-deletions applied to a graph of edge density…
The tree edit distance (TED) between two rooted ordered trees with $n$ nodes labeled from an alphabet $\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of valid operations consisting of insertions, deletions…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the approximate pattern matching problem asks for computation of a particular \emph{distance} function between $P$ and every $m$-substring of $T$. We consider a…
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…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
In this paper, we consider the $k$-approximate pattern matching problem under differential privacy, where the goal is to report or count all substrings of a given string $S$ which have a Hamming distance at most $k$ to a pattern $P$, or…
The work presents two algorithms of manipulation and comparison between strings whose purpose is the orthographic recognition of the apostrophe and of the compound expressions. The theory supporting general reasoning refers to the basic…
We study the online variant of the language distance problem for two classical formal languages, the language of palindromes and the language of squares, and for the two most fundamental distances, the Hamming distance and the edit…