Related papers: Incremental and Fully Dynamic Subgraph Connectivit…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…
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…
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…
We study the \emph{sensitivity oracles problem for subgraph connectivity} in the \emph{decremental} and \emph{fully dynamic} settings. In the fully dynamic setting, we preprocess an $n$-vertices $m$-edges undirected graph $G$ with $n_{\rm…
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…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
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…
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…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
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…
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…
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…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
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…
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…
In multi-agent systems, strong connectivity of the communication network is often crucial for establishing consensus protocols, which underpin numerous applications in decision-making and distributed optimization. However, this connectivity…
Whether a graph $G=(V,E)$ is connected is arguably its most fundamental property. Naturally, connectivity was the first characteristic studied for dynamic graphs, i.e. graphs that undergo edge insertions and deletions. While connectivity…
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…
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…