Related papers: Decompressing Lempel-Ziv Compressed Text
We consider the problem of evaluating regular spanners over compressed documents, i.e., we wish to solve evaluation tasks directly on the compressed data, without decompression. As compressed forms of the documents we use straight-line…
Let $S_{T}(k)$ denote the set of distinct substrings of length $k$ in a string $T$, then the $k$-th substring complexity is defined by its cardinality $|S_{T}(k)|$. Recently, $\delta = \max \{ |S_{T}(k)| / k : k \ge 1 \}$ is shown to be a…
Much research has been devoted to optimizing algorithms of the Lempel-Ziv (LZ) 77 family, both in terms of speed and memory requirements. Binary search trees and suffix trees (ST) are data structures that have been often used for this…
Given a text $T$ and a pattern $P$ over alphabet $\Sigma$, the classic exact matching problem searches for all occurrences of pattern $P$ in text $T$. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the…
Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…
We introduce a compressed suffix array representation that, on a text $T$ of length $n$ over an alphabet of size $\sigma$, can be built in $O(n)$ deterministic time, within $O(n\log\sigma)$ bits of working space, and counts the number of…
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…
We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of…
For decades, computing the LZ factorization (or LZ77 parsing) of a string has been a requisite and computationally intensive step in many diverse applications, including text indexing and data compression. Many algorithms for LZ77 parsing…
The suffix array and the suffix tree are the two most fundamental data structures for string processing. For a length-$n$ text, however, they use $\Theta(n \log n)$ bits of space, which is often too costly. To address this, Grossi and…
In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…
Given two permutations $\sigma$ and $\pi$, the \textsc{Permutation Pattern} problem asks if $\sigma$ is a subpattern of $\pi$. We show that the problem can be solved in time $2^{O(\ell^2\log \ell)}\cdot n$, where $\ell=|\sigma|$ and…
We present RCT, a new compact data structure to represent trajectories of objects. It is based on a relative compression technique called Relative Lempel-Ziv (RLZ), which compresses sequences by applying an LZ77 encoding with respect to an…
Length-$q$ substrings, or $q$-grams, can represent important characteristics of text data, and determining the frequencies of all $q$-grams contained in the data is an important problem with many applications in the field of data mining and…
Relative Lempel-Ziv (RLZ) is a popular algorithm for compressing databases of genomes from individuals of the same species when fast random access is desired. With Kuruppu et al.'s (SPIRE 2010) original implementation, a reference genome is…
We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…
The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the edit-distance between…
Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings,…
The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…
Given a positive \(\epsilon \leq 1\) and read-only access to a string \(S [1..n]\) whose LZ77 parse consists of $z$ phrases, with high probability we can build an LZ77-like parse of $S$ that consists of $\Oh{z / \epsilon}$ phrases using…