Related papers: Fast Computation for the Forest Matrix of an Evolv…

A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…

We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains…

In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…

Visualization is a powerful paradigm for exploratory data analysis. Visualizing large graphs, however, often results in a meaningless hairball. In this paper, we propose a different approach that helps the user adaptively explore large…

Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…

Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…

Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution…

We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…

Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…

We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…

Motifs are the fundamental components of complex systems. The topological structure of networks representing complex systems and the frequency and distribution of motifs in these networks are intertwined. The complexities associated with…

Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static…

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…

Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other methods…

In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks;…

Fast, autonomous flight in unstructured, cluttered environments such as forests is challenging because it requires the robot to compute new plans in realtime on a computationally-constrained platform. In this paper, we enable this…

This paper brings explicit considerations of distributed computing architectures and data structures into the rigorous design of Sequential Monte Carlo (SMC) methods. A theoretical result established recently by the authors shows that…

In Bayesian learning of Gaussian graphical model structure, it is common to restrict attention to certain classes of graphs and approximate the posterior distribution by repeatedly moving from one graph to another, using MCMC or methods…