Related papers: Linear-time Computation of DAWGs, Symmetric Indexi…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning…
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a ``non-trivial'' approximation ratio (as a function of the number of vertices of the input…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…
We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…
The Lyndon array stores, at each position of a word, the length of the longest maximal Lyndon subword starting at that position, and plays an important role in combinatorics on words, for example in the construction of fundamental data…
We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both…
We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…
A growing body of work has begun to study intervention design for efficient structure learning of causal directed acyclic graphs (DAGs). A typical setting is a causally sufficient setting, i.e. a system with no latent confounders, selection…
It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size…
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…
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…
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…
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…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
An algorithm for generating the structure of a directed acyclic graph from data using the notion of causal input lists is presented. The algorithm manipulates the ordering of the variables with operations which very much resemble arc…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
We continue the study of distance sensitivity oracles (DSOs). Given a directed graph $G$ with $n$ vertices and edge weights in $\{1, 2, \dots, M\}$, we want to build a data structure such that given any source vertex $u$, any target vertex…
For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…