Related papers: A well-separated pair decomposition for low densit…
The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to…
Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a…
This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We…
We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…
What is a mathematically rigorous way to describe the taxi-pickup distribution in Manhattan, or the profile information in online social networks? A deep understanding of representing those data not only provides insights to the data…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
In the context of modern machine learning, models deployed in real-world scenarios often encounter diverse data shifts like covariate and semantic shifts, leading to challenges in both out-of-distribution (OOD) generalization and detection.…
Understanding driving scenarios is crucial to realizing autonomous driving. Previous works such as map learning and BEV lane detection neglect the connection relationship between lane instances, and traffic elements detection tasks usually…
We propose the Relational Tucker3 (RT) decomposition for multi-relational link prediction in knowledge graphs. We show that many existing knowledge graph embedding models are special cases of the RT decomposition with certain predefined…
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…