# Random Walker Coverage Analysis for Information Dissemination in Wireless Sensor Networks
## 2 Related Work  
The choice of the model of a geometric random graph to represent WSN and ad hoc networks is quite common in the literature, e.g., [16; 23; 24; 25; 26; 27; 28; 29]. One of the most most comprehensive studies on geometric random graphs can be found in [18] by [PERSON]. In addition, in [30], there is a thorough study on geometric graphs with analytic results (studying graphs of higher dimensions, as well). In this work, [PERSON] and [PERSON] investigate mainly the radius threshold to achieve critical connectivity. The throughput of a mobile ad hoc network powered by energy harvesting is studied and analyzed by [PERSON] [31], using a stochastic, geometric approach. Regarding information dissemination, probabilistic flooding is a popular approach (see for example [32; 33; 34; 35]). Random walkers have been extensively examined in the literature. In particular, in [14], a mathematical framework for random walks on temporal networks is presented by [PERSON] et al. using an approach that provides a compromise between abstract, but unrealistic models and data-driven, but non-mathematical approaches. [PERSON] et al. [15] describe a study on how random walks unfold on temporally-evolving networks with the use of empirical dynamical networks of contacts between individuals. [PERSON] et al. in [16] present the same problem addressed in this work with the technique of a random walker with jumps. [PERSON] et al. in [25] investigate the use of multiple random walkers and related replication mechanisms. Recently, [PERSON] in [36] studied some network properties of WSNs, proposing an improved decision fusion model in order to optimize the energy and bandwidth consumption. [PERSON] et al. [37] explore random geometric graphs and the associated problem of connectivity. In particular, they use the so-called random geometric \"irrigation\" graphs, and then, they provide insightful results on the density of these graphs for a chosen radius. [PERSON] in [38] discusses the behavior of the phase transition of connectivity for geometric random graphs. Random hypergraphs are considered by [PERSON] et al. [39], especially their geometric representations. The authors are concentrated on the probability distribution and its effect on the network topology (and therefore, its properties). Recently, [PERSON] in [40] revisits reviewed related literature on random geometric graphs with a focus on random simplicial complexes. In one of the most recent works related to random walkers on graphs, [PERSON] et al. [41] describe a random walker model where the agent is able to perform long-range hops. This extension seems to reduce the hitting time in comparison to the standard walker. [PERSON] and [PERSON] [29] present an algorithm that improves the data-gathering performance by generating constrained random walks. [PERSON] et al. [17] study non-revisiting random walks. The work of [PERSON] et al. [42] provides an analytical model to evaluate the performance of a random walk-based routing protocol for wireless sensor networks with special attention to two metrics: the mean system data gathering delay and the induced spatial distribution of energy consumption. A forwarding protocol based on biased random walks is proposed combined with a lukewarm potato forwarding protocol that uses local information about neighbors, and their next active period to make forwarding decisions is presented by [PERSON] et al. [24]. A routing protocol based on a random walk is proposed by [PERSON] et al. [43] that achieves load balancing without requiring global location information. [PERSON] et al. [23] present a theoretical approach of random walkers in geometric random graphs that are developed in a \(d\)-dimensional torus. These works, however, do not take into account network coverage as the evolution of time, apart from some special topologies (e.g., fully-connected networks considered in [25]). The work in [12] by [PERSON] and [PERSON] discuss thoroughly the sensing ranges of sensors in wireless sensor networks.