Related papers: The Dynamic k-Mismatch Problem

Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a…

Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local…

In Gapped String Indexing, the goal is to compactly represent a string $S$ of length $n$ such that for any query consisting of two strings $P_1$ and $P_2$, called patterns, and an integer interval $[\alpha, \beta]$, called gap range, we can…

The Knapsack problem is one of the most fundamental NP-complete problems at the intersection of computer science, optimization, and operations research. A recent line of research worked towards understanding the complexity of…

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a $(1+\epsilon)$…

We present new, faster pseudopolynomial time algorithms for the $k$-Subset Sum problem, defined as follows: given a set $Z$ of $n$ positive integers and $k$ targets $t_1, \ldots, t_k$, determine whether there exist $k$ disjoint subsets…

We present streaming algorithms for the graph $k$-matching problem in both the insert-only and dynamic models. Our algorithms, with space complexity matching the best upper bounds, have optimal or near-optimal update time, significantly…

Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit…

A distance matrix $A \in \mathbb R^{n \times m}$ represents all pairwise distances, $A_{ij}=\mathrm{d}(x_i,y_j)$, between two point sets $x_1,...,x_n$ and $y_1,...,y_m$ in an arbitrary metric space $(\mathcal Z, \mathrm{d})$. Such matrices…

$ $We study the $d$-Uniform Hypergraph Matching ($d$-UHM) problem: given an $n$-vertex hypergraph $G$ where every hyperedge is of size $d$, find a maximum cardinality set of disjoint hyperedges. For $d\geq3$, the problem of finding the…

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…

In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance $d_\mathcal{M}$ measures the difference between $2$-parameter persistence modules by taking the…

We consider the problem of preprocessing a text $T$ of length $n$ and a dictionary $\mathcal{D}$ in order to be able to efficiently answer queries $CountDistinct(i,j)$, that is, given $i$ and $j$ return the number of patterns from…

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…

For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete…

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…

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem…