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Edit distance is an important measure of string similarity. It counts the number of insertions, deletions and substitutions one has to make to a string $x$ to get a string $y$. In this paper we design an almost linear-size sketching scheme…

The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…

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…

The shift distance $\mathsf{sh}(S_1,S_2)$ between two strings $S_1$ and $S_2$ of the same length is defined as the minimum Hamming distance between $S_1$ and any rotation (cyclic shift) of $S_2$. We study the problem of sketching the shift…

We provide improved upper bounds for the simultaneous sketching complexity of edit distance. Consider two parties, Alice with input $x\in\Sigma^n$ and Bob with input $y\in\Sigma^n$, that share public randomness and are given a promise that…

We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…

In many applications, it is necessary to determine the similarity of two strings. A widely-used notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one…

We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string $I$. In particular, for every length $n$ and…

Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…

String edit distances have been used for decades in applications ranging from spelling correction and web search suggestions to DNA analysis. Most string edit distances are variations of the Levenshtein distance and consider only…

The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the edit-distance between…

The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit…

We present an algorithm for approximating the edit distance $\operatorname{ed}(x, y)$ between two strings $x$ and $y$ in time parameterized by the degree to which one of the strings $x$ satisfies a natural pseudorandomness property. The…

Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a…

Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually…

In this paper we give an algorithm for streaming $k$-edit approximate pattern matching which uses space $\widetilde{O}(k^2)$ and time $\widetilde{O}(k^2)$ per arriving symbol. This improves substantially on the recent algorithm of…

We present the first one-shot personalized sketch segmentation method. We aim to segment all sketches belonging to the same category provisioned with a single sketch with a given part annotation while (i) preserving the parts semantics…

In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…

The trace reconstruction problem studies the number of noisy samples needed to recover an unknown string $\boldsymbol{x}\in\{0,1\}^n$ with high probability, where the samples are independently obtained by passing $\boldsymbol{x}$ through a…

We show that in the document exchange problem, where Alice holds $x \in \{0,1\}^n$ and Bob holds $y \in \{0,1\}^n$, Alice can send Bob a message of size $O(K(\log^2 K+\log n))$ bits such that Bob can recover $x$ using the message and his…