Related papers: Reaching consensus on a connected graph
This paper focuses on non-asymptotic diffusion time in asynchronous gossip protocols. Asynchronous gossip protocols are designed to perform distributed computation in a network of nodes by randomly exchanging messages on the associated…
In a sensor network, in practice, the communication among sensors is subject to:(1) errors or failures at random times; (3) costs; and(2) constraints since sensors and networks operate under scarce resources, such as power, data rate, or…
We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
In this paper we carry out a stability analysis of a distributed consensus algorithm in presence of link failures. The algorithm combines a new broadcast version of a Push-Sum algorithm, specifically designed for handling link failures,…
Probabilistic zero forcing is a coloring game played on a graph where the goal is to color every vertex blue starting with an initial blue vertex set. As long as the graph is connected, if at least one vertex is blue then eventually all of…
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…
Distributed consensus has been widely studied for sensor network applications. Whereas the asymptotic convergence rate has been extensively explored in prior work, other important and practical issues, including energy efficiency and link…
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus.…
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where…
Distributed consensus protocols provide a mechanism for spreading information within clustered networks, allowing agents and clusters to make decisions without requiring direct access to the state of the ensemble. In this work, we propose a…
We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set $\mathbb N^{[k]}$, the set of all increasing $k$-tuples in $\mathbb N$. These graphs…
A permutation of [n] induces a graph on [n] such that the edges of the graph correspond to inversion pairs of the permutation. This graph is connected if and only if the corresponding permutation is indecomposable. Let s(n,m) denote a…
How can we approximate sparse graphs and sequences of sparse graphs (with unbounded average degree)? We consider convergence in the first $k$ moments of the graph spectrum (equivalent to the numbers of closed $k$-walks) appropriately…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
The Deffuant model is a spatial stochastic model for the dynamics of opinions in which individuals are located on a connected graph representing a social network and characterized by a number in the unit interval representing their opinion.…