Related papers: Prefix Sorting DFAs: a Recursive Algorithm
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
The problem of Text Indexing is a fundamental algorithmic problem in which one wishes to preprocess a text in order to quickly locate pattern queries within the text. In the ever evolving world of dynamic and on-line data, there is also a…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. We show a linear-time algorithm computing a linear-size representation of all the seeds of a word (the number of seeds might be…
We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…
We show how to modify the linear-time construction algorithm for suffix arrays based on induced sorting (Nong et al., DCC'09) such that it computes the array of longest common prefixes (LCP-array) as well. Practical tests show that this…
Array-of-structures (AoS) to structure-of-arrays (SoA) is a classic compiler transformation that improves memory locality and enables data-parallel execution. Existing AoS-to-SoA transformations primarily target regular, array-based…
For the first time we provide a succinct pattern matching index for arbitrary graphs that can be built in polynomial time, which requires less space and answers queries more efficiently than the one in [SODA 2021]. We show that, given an…
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…
A factorization $f_1, \ldots, f_m$ of a string $w$ of length $n$ is called a repetition factorization of $w$ if $f_i$ is a repetition, i.e., $f_i$ is a form of $x^kx'$, where $x$ is a non-empty string, $x'$ is a (possibly-empty) proper…
We consider the problem of constructing a sparse suffix tree (or suffix array) for $b$ suffixes of a given text $T$ of size $n$, using only $O(b)$ words of space during construction time. Breaking the naive bound of $\Omega(nb)$ time for…
Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for…
Suffix arrays encode the lexicographical order of all suffixes of a text and are often combined with the Longest Common Prefix array (LCP) to simulate navigational queries on the suffix tree in reduced space. In space-critical applications…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
Efficient construction of the suffix tree given an input text is an active area of research from the time it was first introduced. Both theoretical computer scientists and engineers tackled the problem. In this paper we focus on the fastest…
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
We propose a B tree representation storing $n$ keys, each of $k$ bits, in either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b) $O(\lg…
Big data, encompassing extensive datasets, has seen rapid expansion, notably with a considerable portion being textual data, including strings and texts. Simple compression methods and standard data structures prove inadequate for…