Related papers: Conjunctive Queries over Trees
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
We discuss the combinatorics of faces of trees in the context of dendroidal sets and develop a systematic treatment of dendroidal anodyne extensions. As the main example and our motivation, we prove the pushout-product property for the…
The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is…
A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example,…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the…
We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language…
We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
Discourse relations bind smaller linguistic units into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked arguments. A more subtle challenge is…
Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that…
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
In this paper we prove a combinatorial theorem for finite labellings of trees, and show that it is equivalent to a theorem for finite covers of metric trees and a fixed point theorem on metric trees. We trace how these connections mimic the…
Answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs) are arguably among the most fundamental tasks in Computer Science. They are classical NP-complete problems. Consequently, the search for tractable…
We study the complexity of answer counting for ontology-mediated queries and for querying under constraints, considering conjunctive queries and unions thereof (UCQs) as the query language and guarded TGDs as the ontology and constraint…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…