Related papers: Ergodic Effects in Token Circulation
The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Our first contribution is a rigorous framework for design and analysis of distributed…
We consider the following load balancing process for $m$ tokens distributed arbitrarily among $n$ nodes connected by a complete graph: In each time step a pair of nodes is selected uniformly at random. Let $\ell_1$ and $\ell_2$ be their…
We study the fundamental problem of information spreading (also known as gossip) in dynamic networks. In gossip, or more generally, $k$-gossip, there are $k$ pieces of information (or tokens) that are initially present in some nodes and the…
We consider the problem of incremental cycle detection and topological ordering in a directed graph $G = (V, E)$ with $|V| = n$ nodes. In this setting, initially the edge-set $E$ of the graph is empty. Subsequently, at each time-step an…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
The best known solutions for $k$-message broadcast in dynamic networks of size $n$ require $\Omega(nk)$ rounds. In this paper, we see if these bounds can be improved by smoothed analysis. We study perhaps the most natural randomized…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
We consider random-access networks with nodes representing transmitter-receiver pairs whose signals interfere with each other depending on their vicinity. Data packets arrive at the nodes over time and form queues. The nodes can be either…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…
Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…