Related papers: Space Lower Bounds for Online Pattern Matching
In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting…
We were asked to debate the value of the cosmological mass-density parameter Omega. Is Omega_m=1 in accordance with the simplest model? Is Omega_m much smaller as indicated by some observations? There is conflicting evidence. We lay out the…
In this work, we consider the problem of pattern matching under the dynamic time warping (DTW) distance motivated by potential applications in the analysis of biological data produced by the third generation sequencing. To measure the DTW…
Although many authors have considered how many ternary comparisons it takes to sort a multiset $S$ of size $n$, the best known upper and lower bounds still differ by a term linear in $n$. In this paper we restrict our attention to online…
We generalize Karp-Rabin string matching to handle multiple patterns in $\mathcal{O}(n \log n + m)$ time and $\mathcal{O}(s)$ space, where $n$ is the length of the text and $m$ is the total length of the $s$ patterns, returning correct…
Despite the NP hardness of acquiring minimum distance $d_m$ for linear codes theoretically, in this paper we propose one experimental method of finding minimum-weight codewords, the weight of which is equal to $d_m$ for LDPC codes. One…
We revisit the $k$-mismatch problem in the streaming model on a pattern of length $m$ and a streaming text of length $n$, both over a size-$\sigma$ alphabet. The current state-of-the-art algorithm for the streaming $k$-mismatch problem, by…
We examine the complexity of the online Dictionary Matching with One Gap Problem (DMOG) which is the following. Preprocess a dictionary $D$ of $d$ patterns, where each pattern contains a special gap symbol that can match any string, so that…
We study space-pass tradeoffs in graph streaming algorithms for parameter estimation and property testing problems such as estimating the size of maximum matchings and maximum cuts, weight of minimum spanning trees, or testing if a graph is…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
We consider the problem of computing a sequence of range minimum queries. We assume a sequence of commands that contains values and queries. Our goal is to quickly determine the minimum value that exists between the current position and a…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…
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…
Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
High-dimensional linear bandits with low-dimensional structure have received considerable attention in recent studies due to their practical significance. The most common structure in the literature is sparsity. However, it may not be…
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…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…