Related papers: Compressed Index with Construction in Compressed S…
Practical data structures for the edit-sensitive parsing (ESP) are proposed. Given a string S, its ESP tree is equivalent to a context-free grammar G generating just S, which is represented by a DAG. Using the succinct data structures for…
Jumbled indexing is the problem of indexing a text $T$ for queries that ask whether there is a substring of $T$ matching a pattern represented as a Parikh vector, i.e., the vector of frequency counts for each character. Jumbled indexing has…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
Indexing highly repetitive texts --- such as genomic databases, software repositories and versioned text collections --- has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive…
The $r$-index (Gagie et al., JACM 2020) represented a breakthrough in compressed indexing of repetitive text collections, outperforming its alternatives by orders of magnitude. Its space usage, $\mathcal{O}(r)$ where $r$ is the number of…
For $0<\delta <1$ a $\delta$-subrepetition in a word is a factor which exponent is less than~2 but is not less than $1+\delta$ (the exponent of the factor is the ratio of the factor length to its minimal period). The $\delta$-subrepetition…
Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures…
A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N…
In the classic longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, over an alphabet of size $\sigma$, and we are asked to find a longest string occurring as a fragment of both $S$ and…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
We show how, given a straight-line program with $g$ rules for a binary string $B$ of length $n$, in $O(g^{2 / 3} n^{4 / 3})$ time we can build a linear-space index such that, given $m$ and $c$, in O(1) time we can determine whether there is…
We show that if DTIME[2^O(n)] is not included in DSPACE[2^o(n)], then, for every set B in PSPACE/poly, all strings x in B of length n can be represented by a string compressed(x) of length at most log(|B^{=n}|)+O(log n), such that a…
In this paper, we present the following results: (1) We propose a new \emph{dynamic compressed index} of $O(w)$ space, that supports searching for a pattern $P$ in the current text in $O(|P| f(M,w) + \log w \log |P| \log^* M (\log N + \log…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
A closed string $u$ is either of length one or contains a border that occurs only as a prefix and as a suffix in $u$ and nowhere else within $u$. In this paper, we present fast $\mathcal{O}(n\log n)$ time algorithms to compute all…
In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…
A central task in string processing is text indexing, where the goal is to preprocess a text (a string of length $n$) into an efficient index (a data structure) supporting queries about the text. Cole, Gottlieb, and Lewenstein (STOC 2004)…
Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text $T$, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in $T$…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
Suppose we are asked to preprocess a string \(s [1..n]\) such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains. In this paper we give a data structure for this problem that takes \(n…