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Covers are a kind of quasiperiodicity in strings. A string $C$ is a cover of another string $T$ if any position of $T$ is inside some occurrence of $C$ in $T$. The shortest and longest cover arrays of $T$ have the lengths of the shortest…
The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…
This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…
Given a pair of strings, the problems of computing their Longest Common Subsequence and Edit Distance have been extensively studied for decades. For exact algorithms, LCS and Edit Distance (with character insertions and deletions) are…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a…
Dynamic analyses are a standard approach to analyzing and testing concurrent programs. Such techniques observe program traces and analyze them to infer the presence or absence of bugs. At its core, each analysis maintains a partial order…
Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…
We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…
The emergence of massive data in recent years brings challenges to automatic statistical inference. This is particularly true if the data are too numerous to be read into memory as a whole. Accordingly, new sampling techniques are needed to…
This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems…
Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
This work introduces the phenomenon of Collective Almost Synchronization (CAS), which describes a universal way of how patterns can appear in complex networks even for small coupling strengths. The CAS phenomenon appears due to the…
An increasing number of scientific applications are making use of irregular data access patterns. An important class of such patterns involve subscripted-subscripts, wherein an array value appears in the index expression of another array.…
In recent years, data selection has emerged as a core issue for large-scale visual-language model pretraining, especially on noisy web-curated datasets. One widely adopted strategy assigns quality scores such as CLIP similarity for each…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…
Given a set of patterns called a dictionary and a text, the dictionary matching problem is a task to find all occurrence positions of all patterns in the text. The dictionary matching problem can be solved efficiently by using the…