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There is growing interest in concept-based models (CBMs) that combine high-performance and interpretability by acquiring and reasoning with a vocabulary of high-level concepts. A key requirement is that the concepts be interpretable.…
We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to C is fixed-parameter…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
The Recognizability Theorem states that if a set of finite graphs is definable by a monadic second-order (MSO) sentence, then it is recognizable with respect to the graph algebra upon which the definition of clique-width is based.…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…
Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of…
We show that #SAT is polynomial-time tractable for classes of CNF formulas whose incidence graphs have bounded symmetric clique-width (or bounded clique-width, or bounded rank-width). This result strictly generalizes polynomial-time…
Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set ${\cal H}$ of forbidden induced subgraphs. We initiate a…
We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Clique-width is a well-known graph parameter. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded clique-width. The same holds for NLC-width. In this paper we study the behavior of clique-width…
Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by…
We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…
The increasing use of complex machine learning models in education has led to concerns about their interpretability, which in turn has spurred interest in developing explainability techniques that are both faithful to the model's inner…
We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments $\mathcal T$, first-order model checking is either fixed parameter tractable or $\textrm{AW}[*]$-hard. This…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…