Related papers: Structured Decompositions: Structural and Algorith…
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…
Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
Hypertree decompositions (HDs), as well as the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHDs) are hypergraph decomposition methods successfully used for…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical…
Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and…
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…
Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A…
Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian…
We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte's tree decomposition of 2-connected graphs into 3-connected blocks.…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
We present a dynamic data structure for representing a graph $G$ with tree-depth at most $D$. Tree-depth is an important graph parameter which arose in the study of sparse graph classes. The structure allows addition and removal of edges…