相关论文: Efficient reversal of transductions of sparse grap…

In this paper we raise the question of how to compress sparse graphs. By introducing the idea of redundancy, we find a way to measure the overlap of neighbors between nodes in networks. We exploit symmetry and information by making use of…

A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…

We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nesetril and Ossona de Mendez. This generalizes several results from the literature,…

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…

There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…

We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…

Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…

Transductive tasks on graphs differ fundamentally from typical supervised machine learning tasks, as the independent and identically distributed (i.i.d.) assumption does not hold among samples. Instead, all train/test/validation samples are…

Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths. These results show a strong link between the properties of these graph classes considered from the point…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…

Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and…

Monadic stability generalizes many tameness notions from structural graph theory such as planarity, bounded degree, bounded tree-width, and nowhere density. The sparsification conjecture predicts that the (possibly dense) monadically stable…

Understanding how a vertex relates to a set of vertices is a fundamental task in graph analysis. Given a graph $G$ and a vertex set $X \subseteq V(G)$, consider the collection of subsets of the form $N(u) \cap X$ where $u$ ranges over all…

Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO)…

Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…