Related papers: Hierarchical Overlap Graph
The key to the text classification task is language representation and important information extraction, and there are many related studies. In recent years, the research on graph neural network (GNN) in text classification has gradually…
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n^2 \log n)$ algorithm to compute the number of pairs of…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
Given a string $T$, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with $e_T$ arcs, taking overall $O(e_T+e_{{\overline{T}}})$ words of space, where ${\overline{T}}$ is the reverse…
Traditional Retrieval-Augmented Generation (RAG) effectively supports single-hop question answering with large language models but faces significant limitations in multi-hop question answering tasks, which require combining evidence from…
Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…
In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…
Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order…
When drawing graphs whose edges and nodes contain text or graphics, such informa tion needs to be displayed without overlaps, either as part of the initial layout or as a post-processing step. The core problem in removing overlaps lies in…
Graph-based Retrieval-Augmented Generation (GraphRAG) enhances LLMs by structuring corpus into graphs to facilitate multi-hop reasoning. While recent lightweight approaches reduce indexing costs by leveraging Named Entity Recognition (NER),…
Environment representations endowed with sophisticated semantics are pivotal for facilitating seamless interaction between robots and humans, enabling them to effectively carry out various tasks. Open-vocabulary maps, powered by…
Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to…
Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
An Horizontal Visibility Graph (for short, HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between…
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure.…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…