Related papers: Computing String Covers in Sublinear Time

It is shown that for a given ordered node-labelled tree of size $n$ and with $s$ many different node labels, one can construct in linear time a top dag of height $O(\log n)$ and size $O(n / \log_\sigma n) \cap O(d \cdot \log n)$, where…

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…

In this paper, we introduce zip-tries, which are simple, dynamic, memory-efficient data structures for strings. Zip-tries support search and update operations for $k$-length strings in $\mathcal{O}(k+\log n)$ time in the standard RAM model…

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…

We consider the problem of computing the q-gram profile of a string \str of size $N$ compressed by a context-free grammar with $n$ production rules. We present an algorithm that runs in $O(N-\alpha)$ expected time and uses $O(n+q+\kq)$…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

In this paper we describe compressed indexes that support pattern matching queries for strings with wildcards. For a constant size alphabet our data structure uses $O(n\log^{\varepsilon}n)$ bits for any $\varepsilon>0$ and reports all…

A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…

For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg…

We show that the Longest Common Prefix Array of a text collection of total size n on alphabet [1, {\sigma}] can be computed from the Burrows-Wheeler transformed collection in O(n log {\sigma}) time using o(n log {\sigma}) bits of working…

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically…

An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their…

Let a text $T[1..n]$ be the only string generated by a context-free grammar with $g$ (terminal and nonterminal) symbols, and of size $G$ (measured as the sum of the lengths of the right-hand sides of the rules). Such a grammar, called a…

Let $s$ be a string of length $n$ over an alphabet of constant size $\sigma$ and let $c$ and $\epsilon$ be constants with (1 \geq c \geq 0) and (\epsilon > 0). Using (O (n)) time, (O (n^c)) bits of memory and one pass we can always encode…

Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse…

We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…

Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximum-sum segment queries on A: i.e., given an arbitrary range [i,j], return the subrange [i' ,j' ] \subseteq [i,j] such…

The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…