We present an algorithm for approximating the edit distance between two strings of length n
in time n 1+ ε, for any, up to a constant factor. Our result completes a research direction set …

Measuring sequence similarity and compressing texts are among the most fundamental
tasks in string algorithms. In this work, we develop near-optimal quantum algorithms for the …

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 …

The edit distance (also known as Levenshtein distance) of two strings is the minimum
number of insertions, deletions, and substitutions of characters needed to transform one …

We study the problem of approximating edit distance in sublinear time. This is formalized as
the (k,\k^c)-GAP EDIT DISTANCE problem, where the input is a pair of strings X,Y and …

We study the problem of approximating the edit distance of two strings in sublinear time, in a
setting where one or both string (s) are preprocessed, as initiated by Goldenberg …

The edit distance of two strings is the minimum number of insertions, deletions, and
substitutions needed to transform one string into the other. The textbook algorithm …

In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-
sensitive and sublinear-time algorithms for two important problems.(1) Sparse Convolution …

In the Massively Parallel Computation (MPC) model, data is distributed across multiple
processors, and we call an algorithm space-efficient if each machine has n^ 1-ε+ o (1) …

The edit distance between strings classically assigns unit cost to every character insertion,
deletion, and substitution, whereas the Hamming distance only allows substitutions. In many …