Parsimonious Flooding in Geometric Random-Walks

Abstract

• We analyze the Parsimonious-Flooding Protocol on Mobile Opportunistic Networks yielded by the Geometric Random-Walk Model.• For the first time, we provide analytical bounds on the completion time. Such bounds are optimal for a wide range of the network parameters.• Departing significantly from previous analysis of the standard flooding protocol, our proof technique determines the geometric shape of the information spreading (i.e. the infection wave) over the time. June 3, 2014 AbstractWe study the epidemic process yielded by the k-Flooding Protocol in geometric Mobile Ad-Hoc Networks. We consider n agents on a square performing independent random walks. At any time step, every active agent informs every non-informed agent which is within distance R from it. An informed agent is active only for k time steps. Initially, a source agent is informed and we look at the completion time of the protocol. We prove optimal bounds on the completion time of the process. Our method of analysis provides a clear picture of the geometric shape of the information spreading over the time.

Latency-optimized broadcast in mobile ad hoc networks without node coordination

“…mobility model [29], the random walk model [38], etc. In the dense regime where the transmission radius is above the critical radius, Clementi et al did several work under an almost the same network model as studied in our work [7,8,9]. They established a lower bound on the broadcast latency, and analyzed the broadcast latency under the flooding approach without taking the interference into account.…”

“…Here we mean two ρ-cells (or two r-cells which are defined later) are adjacent if they touch each other by a side or by a corner. This mobility model can be viewed as a discrete version of the random walk mobility model, and has been widely used in literatures, e.g., [9,5]. In particular, when ρ = √ n/3, this model degenerates to be the well-known i.i.d.…”

“…Let Z be the number of r-cells that contain one or more μ-informed nodes after the move phase of time slot t + 1. According to [9], there exists some constants ϕ1 and ψ1 such that…”

Dynamic Hidden-Variable Network Models

“…A model with both dynamic HVs and persistent links [141] was recently introduced, alongside rigorous inference techniques and applications -but not in reference to static network models. Other studies investigated spreading on dynamic RGG-like graphs [79,109]. A few versions of dynamic SBMs are of particular relevance; in one such paper [72], the model is a case of the temporal hyper-SBM studied in Section V A with complete edge-resampling (ω = 1).…”

“…The family of models we introduce is demonstrated to have wide generality, as exemplified by temporal extensions of four different static models with hidden variables: stochastic block models [20], random geometric graphs [21], soft configuration models [22], and hyperbolic graphs [15]. These examples relate to, and partially encompass, several models of networks with dynamic node-properties that have been previously studied -for instance dynamic latent space models [74][75][76][77], dynamic random geometric graphs [78,79], and dynamic stochastic block models [72,73]. The framework we study is also widely generalizable to other contexts.…”