Related papers: Size-constrained Weighted Ancestors with Applicati…
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 problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
We show how to build several data structures of central importance to string processing, taking as input the Burrows-Wheeler transform (BWT) and using small extra working space. Let $n$ be the text length and $\sigma$ be the alphabet size.…
We investigate the nearest common ancestor (NCA) function in rooted trees. As the main conceptual contribution, the paper introduces universal trees for the NCA function: For a given family of rooted trees, an NCA-universal tree $S$ is a…
Phylogenetic trees represent certain species and their likely ancestors. In such a tree, present-day species are leaves and an edge from u to v indicates that u is an ancestor of v. Weights on these edges indicate the phylogenetic distance.…
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…
Search trees on trees (STTs) generalize the fundamental binary search tree (BST) data structure: in STTs the underlying search space is an arbitrary tree, whereas in BSTs it is a path. An optimal BST of size $n$ can be computed for a given…
A labeled tree (or a trie) is a natural generalization of a string, which can also be seen as a compact representation of a set of strings. This paper considers the labeled tree indexing problem, and provides a number of new results on…
Reconstructing ancestral gene orders in a given phylogeny is a classical problem in comparative genomics. Most existing methods compare conserved features in extant genomes in the phylogeny to define potential ancestral gene adjacencies,…
A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case…
Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…
We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…
A level-ancestor or LA query about a rooted tree $T$ takes as arguments a node $v$ in $T$, of depth $d_v$, say, and an integer $d$ with $0\le d\le d_v$ and returns the ancestor of $v$ in $T$ of depth $d$. The static LA problem is to process…
We study two fundamental decremental dynamic graph problems. In both problems, we need to maintain a vertex-weighted forest of size $n$ under edge deletions, weight updates, and a certain information-retrieval query. Both problems can be…
The largest common embeddable subtree problem asks for the largest possible tree embeddable into two input trees and generalizes the classical maximum common subtree problem. Several variants of the problem in labeled and unlabeled rooted…
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…