Related papers: Range Predecessor and Lempel-Ziv Parsing
It was recently proved that any SLP generating a given string $w$ can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We show that this result also holds for RLSLPs, which are SLPs extended with…
This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…
The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length…
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…
At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…
In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. This type of structures was investigated…
For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in…
The Lempel-Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robustness of this property under small violations of ergodicity is studied. A notion of deficiency of…
Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we…
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…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…
In the range $\alpha$-majority query problem, we are given a sequence $S[1..n]$ and a fixed threshold $\alpha \in (0, 1)$, and are asked to preprocess $S$ such that, given a query range $[i..j]$, we can efficiently report the symbols that…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings,…
Given a string $T$ of length $N$, the goal of grammar compression is to construct a small context-free grammar generating only $T$. Among existing grammar compression methods, RePair (recursive paring) [Larsson and Moffat, 1999] is notable…
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…
A compressed self-index stores a string in compressed form while supporting locate queries without decompression. For highly repetitive strings (arising in web crawls, versioned documents, and genomic collections), static self-indexes can…
We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…
We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…