Related papers: Distributed Connectivity Decomposition
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
We present a data structure that, given a graph $G$ of $n$ vertices and $m$ edges, and a suitable pair of nested $r$-divisions of $G$, preprocesses $G$ in $O(m+n)$ time and handles any series of edge-deletions in $O(m)$ total time while…
We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
We introduce a new network statistic that measures diverse structural properties at the micro-, meso-, and macroscopic scales, while still being easy to compute and easy to interpret at a glance. Our statistic, the onion spectrum, is based…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…
We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…
We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_{\star}$ failed vertices in $\tilde{O}(d^3)$ time and thereafter…
The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…