Related papers: Fast Consensus over Almost Regular Directed Graphs
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
We present DMaC, a novel distributed, finite-time algorithm that guarantees max-consensus in directed networks with unreliable communication links experiencing packet drops. Unlike existing methods, DMaC ensures all nodes compute the exact…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
We address the problem of finding the nearest graph Laplacian to a given matrix, with the distance measured using the Frobenius norm. Specifically, for the directed graph Laplacian, we propose two novel algorithms by reformulating the…
The design of sensor networks capable of reaching a consensus on a globally optimal decision test, without the need for a fusion center, is a problem that has received considerable attention in the last years. Many consensus algorithms have…
We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$,…
The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest…
Inspired by distributed resource allocation problems in dynamic topology networks, we initiate the study of distributed consensus with finite messaging passing. We first find a sufficient condition on the network graph for which no…
Consensus is arguably the most studied problem in distributed computing as a whole, and particularly in the distributed message-passing setting. In this latter framework, research on consensus has considered various hypotheses regarding the…
Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
I extend the methods in "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng" to directed graphs with a variation of…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
In this paper we consider the following problem: Over the class of all simple connected graphs of order $n$ with $k$ pendant vertices ($n,k$ being fixed), which graph maximizes (respectively, minimizes) the algebraic connectivity? We also…
In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…
In this paper, we address the discrete-time average consensus problem in strongly connected directed graphs, where nodes exchange information over unreliable error-prone communication links. We enhance the Robustified Ratio Consensus…
In this paper we introduce a notion of spectral approximation for directed graphs. While there are many potential ways one might define approximation for directed graphs, most of them are too strong to allow sparse approximations in…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…