相关论文: $k$-local Graphs

Modern graph clustering applications require the analysis of large graphs and this can be computationally expensive. In this regard, local spectral graph clustering methods aim to identify well-connected clusters around a given "seed set"…

Spatial co-location pattern mining refers to the task of discovering the group of objects or events that co-occur at many places. Extracting these patterns from spatial data is very difficult due to the complexity of spatial data types,…

The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding…

Finding a list of k teams of experts, referred to as top-k team formation, with the required skills and high collaboration compatibility has been extensively studied. However, existing methods have not considered the specific collaboration…

Nearest neighbor search has found numerous applications in machine learning, data mining and massive data processing systems. The past few years have witnessed the popularity of the graph-based nearest neighbor search paradigm because of…

The $k$-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct $k$-NN graphs remains a challenge, especially for…

Node coloring is the task of assigning colors to the nodes of a graph such that no two adjacent nodes have the same color, while using as few colors as possible. It is the most widely studied instance of graph coloring and of central…

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…

Graph Neural Networks have shown excellent performance on semi-supervised classification tasks. However, they assume access to a graph that may not be often available in practice. In the absence of any graph, constructing k-Nearest Neighbor…

Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…

The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of large independent sets, of size matching the best-known…

In this paper we propose a deterministic algorithm for approximately counting the $k$-colourings of sparse random graphs $G(n,d/n)$. In particular, our algorithm computes in polynomial time a $(1\pm n^{-\Omega(1)})$approximation of the…

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…

We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that…

The classical global criteria for the existence of Hamilton cycles only apply to graphs with large edge density and small diameter. In a series of papers Asratian and Khachatryan developed local criteria for the existence of Hamilton cycles…

Graph neural networks (GNNs) emerge as a powerful family of representation learning models on graphs. To derive node representations, they utilize a global model that recursively aggregates information from the neighboring nodes. However,…

The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an…

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper…

We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…