Related papers: Local Hyper-Flow Diffusion
The analysis of networks, aimed at suitably defined functionality, often focuses on partitions into subnetworks that capture desired features. Chief among the relevant concepts is a 2-partition, that underlies the classical Cheeger…
The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here…
We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…
We study the problem of self-supervised 3D scene flow estimation from real large-scale raw point cloud sequences, which is crucial to various tasks like trajectory prediction or instance segmentation. In the absence of ground truth scene…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic $O(m \log^2 n \log\log^2 n)$ time algorithm. This improves both on the best previously known deterministic running time of $O(m \log^{12}…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. There could be clustering (beyond homophily) at a macro level as well as transitivity (a friend's friend is more…
In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
Clustering nodes in heterophilous graphs is challenging as traditional methods assume that effective clustering is characterized by high intra-cluster and low inter-cluster connectivity. To address this, we introduce HeNCler-a novel…
We study a continuous-time primal-dual algorithm for distributed optimization with nonconvex local cost functions over weight-unbalanced digraphs, and analyze its performance from a dissipativity-based perspective. We first reformulate the…
The heat kernel is a particular type of graph diffusion that, like the much-used personalized PageRank diffusion, is useful in identifying a community nearby a starting seed node. We present the first deterministic, local algorithm to…
Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…