Related papers: Dynamic Connectivity: Connecting to Networks and G…
Real-world networks are prone to breakdowns. Typically in the underlying graph $G$, besides the insertion or deletion of edges, the set of active vertices changes overtime. A vertex might work actively, or it might fail, and gets isolated…
Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and…
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…
In the fully dynamic edge connectivity problem, the input is a simple graph $G$ undergoing edge insertions and deletions, and the goal is to maintain its edge connectivity, denoted $\lambda_G$. We present two simple randomized algorithms…
During the last 10 years it has become popular to study dynamic graph problems in a emergency planning or sensitivity setting: Instead of considering the general fully dynamic problem, we only have to process a single batch update of size…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a…
We give offline algorithms for processing a sequence of $2$ and $3$ edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for $3$-edge and $3$-vertex…
We present new results on a number of fundamental problems about dynamic geometric data structures: 1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or…
We present the first fully dynamic connectivity data structures for geometric intersection graphs achieving constant query time and sublinear amortized update time for most types of geometric objects in 2D. Our data structures can answer…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
We present a deterministic fully-dynamic data structure for maintaining information about the cut-vertices in a graph; i.e. the vertices whose removal would disconnect the graph. Our data structure supports insertion and deletion of edges,…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs.…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
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 this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let $G$ be a digraph with $m$ edges and $n$ vertices, and let $G\setminus e$ be the digraph obtained after deleting edge $e$ from $G$. As a first…
In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions…