相关论文: On Descriptional Complexity of the Planarity Probl…

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…

Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…

Explainability techniques for Graph Neural Networks still have a long way to go compared to explanations available for both neural and decision decision tree-based models trained on tabular data. Using a task that straddles both graphs and…

We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

Graph neural networks (GNNs) have demonstrated a significant boost in prediction performance on graph data. At the same time, the predictions made by these models are often hard to interpret. In that regard, many efforts have been made to…

Computing the crossing number of a graph is one of the most classical problems in computational geometry. Both it and numerous variations of the problem have been studied, and overcoming their frequent computational difficulty is an active…

This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.

It is unclear whether, how and where large pre-trained language models capture subtle linguistic traits like ambiguity, grammaticality and sentence complexity. We present results of automatic classification of these traits and compare their…

Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…

The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing. Several bounds on the…

In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…

Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…

After a period of decrease, interest in word alignments is increasing again for their usefulness in domains such as typological research, cross-lingual annotation projection, and machine translation. Generally, alignment algorithms only use…

We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…

A (smooth) embedding of a closed curve on the plane with finitely many intersections is said to be generic if each point of self-intersection is crossed exactly twice and at non-tangent angles. A finite word $\omega$ where each character…

Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. Aim of this survey is to describe the main research…

The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…

For an arbitrary word $w$ on an alphabet, we can define the alternating symbol graph, $G(w)$, as the graph in which the edge $(a, b)$ is in $E$ iff the letters $a$ and $b$ alternate in the word $w$. A graph $G = (V, E)$ is said to be…