Related papers: Network Localization on Unit Disk Graphs
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…
Memory is an important cognitive function for humans. How a brain with such a small power can complete such a complex memory function, the working mechanism behind this is undoubtedly fascinating. Engram theory views memory as the…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
Cooperative localization leverages noisy inter-node distance measurements and exchanged wireless messages to estimate node positions in a wireless network. In communication-constrained environments, however, transmitting large messages…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_i, i=1,\ldots,n$, with each graph consisting…
How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…
We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…
We consider the fundamental problem of decomposing a large-scale approximate nearest neighbor search (ANNS) problem into smaller sub-problems. The goal is to partition the input points into neighborhood-preserving shards, so that the…
We present an algorithm which computes a planar 2-spanner from an Unit Disk Graph when the node density is sufficient. The communication complexity in terms of number of node's identifier sent by the algorithm is $6n$, while the…
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the "search" problem of this paper aims to only find the nodes in a "single" such…
Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
Representation of large data sets became a key question of many scientific disciplines in the last decade. Several approaches for network visualization, data ordering and coarse-graining accomplished this goal. However, there was no…