Related papers: Dynamic Connectivity: Connecting to Networks and G…
Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to…
SPQR-trees are a central component of graph drawing and are also important in many further areas of computer science. From their inception onwards, they have always had a strong relation to dynamic algorithms maintaining information, e.g.,…
Connectivity queries, which check whether vertices belong to the same connected component, are fundamental in graph computations. Sliding window connectivity processes these queries over sliding windows, facilitating real-time streaming…
We study dynamic algorithms for maintaining fundamental algebraic properties of matrices, specifically, rank, basis, and full-rank submatrices, with applications to maximum matching on dynamic graphs. Prior dynamic algorithms for rank…
We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
Researchers, policy makers, and engineers need to make sense of data from spreading processes as diverse as rumor spreading in social networks, viral infections, and water contamination. Classical questions include predicting infection…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
A stable cutset is a set of vertices $S$ of a connected graph, that is pairwise non-adjacent and when deleting $S$, the graph becomes disconnected. Determining the existence of a stable cutset in a graph is known to be NP-complete. In this…
Finding central nodes is a fundamental problem in network analysis. Betweenness centrality is a well-known measure which quantifies the importance of a node based on the fraction of shortest paths going though it. Due to the dynamic nature…
We investigate online network topology identification from smooth nodal observations acquired in a streaming fashion. Different from non-adaptive batch solutions, our distinctive goal is to track the (possibly) dynamic adjacency matrix with…
The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…
Given a query graph that represents a pattern of interest, the emerging pattern detection problem can be viewed as a continuous query problem on a dynamic graph. We present an incremental algorithm for continuous query processing on dynamic…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…