Related papers: FO and MSO Model Checking on Temporal Graphs
Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We…
We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
For every $q\in \mathbb N$ let $\textrm{FO}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{FO}_q$, then it can be decided in time $O(n^q)$. Thus,…
We study the computational complexity of the FO model checking problem on interval graphs, i.e., intersection graphs of intervals on the real line. The main positive result is that FO model checking and successor-invariant FO model checking…
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…
Dynamic networks reflect temporal changes occurring to the graph's structure and are used to model a wide variety of problems in many application fields. We investigate the design space of dynamic graph visualization along two major…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
For a finite collection of graphs ${\cal F}$, the \textsc{${\cal F}$-TM-Deletion} problem has as input an $n$-vertex graph $G$ and an integer $k$ and asks whether there exists a set $S \subseteq V(G)$ with $|S| \leq k$ such that $G…
Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…
We present the Temporal Graph Benchmark (TGB), a collection of challenging and diverse benchmark datasets for realistic, reproducible, and robust evaluation of machine learning models on temporal graphs. TGB datasets are of large scale,…
We present a first-order linear-time temporal logic for reasoning about the evolution of directed graphs. Its semantics is based on the counterpart paradigm, thus allowing our logic to represent the creation, duplication, merging, and…
Algorithmic meta-theorems, stating that graph properties expressible in some particular logic can be decided efficiently in graph classes having some specific structural properties, are now standard in sequential graph algorithms. One of…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
Answering time-sensitive questions from long documents requires temporal reasoning over the times in questions and documents. An important open question is whether large language models can perform such reasoning solely using a provided…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…
Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging…
A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…
We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…
In this work, we introduce a filtration on temporal graphs based on $\delta$-temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered…