Related papers: Graph Algorithms for Improving Type-Logical Proof …
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…
We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the clique width of a graph is bounded in terms of its rank width, we also obtain a polynomial time isomorphism test…
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically…
Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying…
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…
Graph neural networks (GNNs) are popular to use for classifying structured data in the context of machine learning. But surprisingly, they are rarely applied to regression problems. In this work, we adopt GNN for a classic but challenging…
The problem of listing the $K$ shortest simple (loopless) $st$-paths in a graph has been studied since the early 1960s. For a non-negatively weighted graph with $n$ vertices and $m$ edges, the most efficient solution is an $O(K(mn + n^2…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Knitting, an ancient fiber art, creates a structured fabric consisting of loops or stitches. Publishing hand knitting patterns involves lengthy testing periods and numerous knitters. Modeling knitting patterns with graphs can help expedite…
Recent advances in search-augmented large reasoning models (LRMs) enable the retrieval of external knowledge to reduce hallucinations in multistep reasoning. However, their ability to operate on graph-structured data, prevalent in domains…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Fact checking is a challenging task because verifying the truthfulness of a claim requires reasoning about multiple retrievable evidence. In this work, we present a method suitable for reasoning about the semantic-level structure of…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal…
ChatGPT said: Text-attributed graphs, where nodes and edges contain rich textual information, are widely used across diverse domains. A central challenge in this setting is question answering, which requires jointly leveraging unstructured…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based…