Related papers: Quadratic Conditional Lower Bounds for String Prob…
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…
We prove 3SUM-hardness (no strongly subquadratic-time algorithm, assuming the 3SUM conjecture) of several problems related to finding Abelian square and additive square factors in a string. In particular, we conclude conditional optimality…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in…
A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…
We introduce string2string, an open-source library that offers a comprehensive suite of efficient algorithms for a broad range of string-to-string problems. It includes traditional algorithmic solutions as well as recent advanced neural…
A weighted string, also known as a position weight matrix, is a sequence of probability distributions over some alphabet. We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is,…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
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…
Gibbons and Korach studied a fundamental problem in 1997: given an observed sequence of reads and writes of a multi-threaded program, does there exist an interleaving which is sequentially consistent? Apart from applications in testing…
The (unweighted) tree edit distance problem for $n$ node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in $O(n ^ 3)$ time [Demaine,…
In this work, we study the relative hardness of fundamental problems with state-of-the-art word RAM algorithms that take $O(n\sqrt{\log n})$ time for instances described in $\Theta(n)$ machine words ($\Theta(n\log n)$ bits). This complexity…
This paper proposes a general framework for matching similar subsequences in both time series and string databases. The matching results are pairs of query subsequences and database subsequences. The framework finds all possible pairs of…
The edit distance is a way of quantifying how similar two strings are to one another by counting the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. In this paper we…
Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…
We consider the following string matching problem on a node-labeled graph $G=(V,E)$: given a pattern string $P$, decide whether there exists a path in $G$ whose concatenation of node labels equals $P$. This is a basic primitive in various…
In the classic polyline simplification problem we want to replace a given polygonal curve $P$, consisting of $n$ vertices, by a subsequence $P'$ of $k$ vertices from $P$ such that the polygonal curves $P$ and $P'$ are as close as possible.…
The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…
We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively…
We present a randomized algorithm that computes a constant approximation of a graph's arboricity, using $\tilde{O}(n/\lambda)$ queries to adjacency lists and in the same time bound. Here, $n$ and $\lambda$ denote the number of nodes and the…
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is, for example, common in Molecular Dynamics, where one aims…