CriticalDensityforExposure-PathPreventioninThree-DimensionalWirelessSensorNetworksUsingPercolationTheory资源-CSDN文库

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### 关键密度与暴露路径预防在三维无线传感器网络中的应用 #### 概述本文献主要探讨了在三维无线传感器网络（3D WSNs）中实现暴露路径预防的关键密度问题，并采用渗透理论来建立相应的数学模型。研究由北京邮电大学的康桂霞、刘晓爽、张宁波、郭艳艳以及法布里斯·拉博共同完成。该研究通过提出一种基于键渗透的方案，能够计算出暴露路径预防所需的关键密度的更精确下限与上限。 #### 研究背景与意义在过去几十年里，无线传感器网络（WSNs）已成为一项引人注目的技术，并催生了包括通信协议和硬件平台在内的多个研究领域。WSNs的应用范围广泛，从军事应用到健康环境监测、地震监控等都有其身影。在这类应用场景中，一个关键问题是确保传感器节点能够有效地检测到感兴趣的区域内发生的入侵行为。因此，如何准确地确定传感器节点在三维空间中的部署密度，以确保有效覆盖并及时检测到入侵路径，成为了一个重要的研究课题。 #### 主要研究内容本研究首先介绍了暴露路径预防问题及基于高斯分布的系统模型。在此基础上，依据渗透理论，研究者提出了一个键渗透模型，将暴露路径预防问题映射到了三维均匀晶格中。通过这一模型，研究团队推导出了三维无线传感器网络中暴露路径预防所需的关键密度的上下界。此外，为了验证所提出的模型的有效性及评估提议方案的性能，研究还进行了广泛的模拟实验和对比实验。 #### 理论框架与方法 - **暴露路径预防问题介绍**：研究定义了暴露路径预防问题，即如何通过合理布置传感器节点来确保任何可能的入侵路径都被检测到。 - **系统模型**：基于高斯分布的系统模型被用来描述传感器的覆盖能力和检测概率。 - **键渗透模型**：研究采用了键渗透模型作为数学工具，通过分析三维均匀晶格中键的存在与否来模拟传感器节点之间的连接性和覆盖情况。 - **关键密度的推导**：利用键渗透模型，研究者推导出了三维无线传感器网络中实现暴露路径预防所需的关键密度的上下限。 #### 实验结果与讨论 - **模拟实验**：通过大量的模拟实验验证了所提出的模型的有效性。这些实验结果显示，所提出的键渗透模型能够准确地预测关键密度的范围。 - **对比实验**：通过与其他已有的方法进行比较，进一步证实了本研究所提出的方案在提高网络覆盖率和降低部署成本方面的优势。 #### 结论本文献提出了一种基于键渗透理论的方法，用于确定三维无线传感器网络中实现暴露路径预防所需的最小关键密度。该方法不仅能够提供更精确的关键密度范围估计，而且还通过广泛的实验验证了其有效性。这对于实际应用中的传感器网络设计和部署具有重要意义。未来的研究可以进一步探索如何优化节点部署策略，以提高系统的整体性能和可靠性。

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Research Article

Critical Density for Exposure-Path Prevention in

Three-Dimensional Wireless Sensor Networks Using

Percolation Theory

Guixia Kang, Xiaoshuang Liu, Ningbo Zhang, Yanyan Guo, and Fabrice Labeau

Key Laboratory of Universal Wireless Communication, Ministry of Education, Beijing University of Posts and Telecommunications,

Beijing 100876, China

Correspondence should be addressed to Xiaoshuang Liu; lxs

55@163.com

Received 24 August 2014; Accepted 14 December 2014

Academic Editor: Eleana Asimakopoulou

permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To derive the critical density for exposure-path prevention in three-dimensional wireless sensor networks (3D WSNs), a bond-

percolation-based scheme is proposed, which can generate the tighter lower and upper bounds of critical density. Firstly, the

exposure-path prevention problem and system models based on Gaussian distribution are introduced in this paper. en, according

to percolation theory, we present a bond-percolation model to put this problem into a 3D uniform lattice. With this model, the

lower and upper bounds of critical density for 3D WSNs are derived in the light of our scheme. Extensive simulations and contrast

experiments also validate our developed models and evaluate the performance of the proposed schemes. erefore, our scheme

can be applied to determine a practically reliable density and detect intruders in sensor networks.

1. Introduction

Over the past decades, wireless sensor networks (WSNs)

have represented one of the most outstanding technologies,

and several research disciplines, such as communication

protocols, and hardware platforms, have appeared to cover

the special requirements of these systems. Many applications

of WSNs need the intrusions being detected by sensor

nodes in the interested region [1], like military applications,

healthy environment monitoring, seism surveillance, and

so on. e intrusion detection problem belongs to node

coverage issue that is vital in the area of WSNs. Moreover, if

nodes detect intrusion paths, the intrusions can be detected.

Namely,coverageofintrusionpathshasimportantinuence

in detecting intrusions.

Generally, coverage reects QoS (quality of service) pro-

vided by sensor nodes of networks [2]. It creates collabo-

rations among the nodes in covering an interested region

for monitoring specic information. e researchers have

studied the coverage problem from many dierent perspec-

tives based on dierent requirements [3, 4]. As shown in

the majority of references [2–4], if each point in the region

is sensed by at least one sensor node, this region is dened

as covered region. However, if the objective of coverage is

to detect moving targets or phenomena, the traditional full

coverage model [2–4] may be unnecessary. Full coverage

means that everywhere in the deployment area is covered

by nodes, which is at the cost of resource wastes and high

complexity [5]. But coverage for intrusion detection only

needs partial coverage ensuring that no moving targets or

phenomena can pass through the interested region without

being detected [6]. If an intruder can traverse through the

deployment area and the resulting path is not covered by

nodes, we name the traversed path as the exposure path.

It reects the ability of intrusions moving through the

deployed area [7]. Preventing the exposure paths belongs to

the exposure-path prevention problem. On account of the full

coverage, network coverage is rather poor if there exists an

exposure path in WSNs [8]. Hence, this paper considers the

problemofnoexposurepathin3DWSNs.

To address the exposure-path problem, this paper adopts

percolation theory [9–11] to compute the optimal density in

order to make the probability of an exposure path existing

converge to 0 and satisfy the minimum density of sensor

Hindawi Publishing Corporation

International Journal of Distributed Sensor Networks

Article ID 738974 12 pages

http://dx.doi.org/10.1155/2015/738974

2 International Journal of Distributed Sensor Networks

nodes. In [12], Broadbent and Hammersley rst introduced

percolation theory to model the disordered media and sim-

ulate the percolation process of immersed rocks. Since this

theory reveals the vital relationships between probabilistic

and topological characteristics of graphs, it is attractive to

researchers [13]andhasbeenusedtostudyconnectivityof

WSNs [14–16]. In this paper, we exploit the percolation theory

to obtain the optimal density for coverage inomnidirectional

sensor networks.

On the basis of percolation theory [10, 13], if is the

average degree of connectivity between various subunits of

some arbitrary system, there exists a percolation threshold,

denoted by 

𝑡

.When≥

𝑡

,thereisnoexposurepathfrom

one side to the other side of this system, and not vice versa.

Deriving the critical density to achieve regional coverage

for random network deployment process is a fundamentally

important problem in the area of WSNs. Based on percolation

theory, most existing studies [14–16] apply the continuum-

percolation theory to derive the optimal density for coverage.

However, the studies suer from the loose lower and upper

bounds of critical density and cannot be applied to determine

a practically useful density for network deployment. In this

paper, a bond-percolation scheme is proposed in 3D WSNs

toconquertheaboveproblemandmakepercolationtheory

more suitable for the exposure-path problem. We assume

sensor nodes deployed under a 3D Gaussian process, and the

rigorous derivation analyses and simulation results indicate

that the proposed method can generate much tighter upper

and lower bounds of critical density.

e remainder of our paper is structured as follows.

Section 2 introducestherelatedworks,andbasedonGaus-

sian distribution, Section 3 presents the system models and

problem formulation about exposure-path prevention in 3D

WSNs. Section 4 describes the bond-percolation theory to

derive and analyze the optimal critical density for exposure-

path problem. In addition, the mutual dependence among

edges of the proposed scheme is dealt with in this section.

In Section 5, extensive simulation results evaluate the models

and schemes we proposed, and the last section concludes this

paper.

2. Related Works

In this section, we introduce the related works of percolation

theory and exposure-path problem in WSNs. Due to coverage

of exposure paths belonging to barrier coverage, this section

also presents recent results about barrier coverage.

e coverage of WSNs can be classied into three types:

area coverage, barrier coverage, and point coverage in terms

of the dierent covered objects [17]. Area coverage is full

coverage, while barrier coverage and point coverage are

partial coverage. Area coverage needs every point within

the target area covered by at least one node [18]; barrier

coverage measures the detection ability [19]; point coverage

requires the coverage of several discrete targets [20]. In this

paper, barrier coverage contains the mentioned exposure-

path problem. Next, we introduce the related researches on

exposure-path problem.

In [21], the authors provided formal yet intuitive for-

mulations, established the complexity of the exposure-path

problem and developed practical algorithms for exposure cal-

culation. ey also investigated the relationship and interplay

of exposure problem with other fundamental wireless sensor

networktasksandinparticularwithlocationdiscovery

and deployment. Aer elucidating the importance of the

exposure problem, Megerian et al. [22] formally dened

exposure paths and studied exposure-path properties. Mean-

while, they developed an ecient-eective algorithm for

exposure calculations in sensor networks, specically for

nding minimum exposure paths. Veltri et al. [23]proposed

an ecient localized algorithm enabling a sensor network to

determine its minimum exposure path. eoretical highlight

of this reference is the closed-form solution for minimum

exposure in the presence of a single sensor node. Moreover,

they introduced a new coverage problem, the maximum

exposure path, which was proved NP-hard and could be

resolved by heuristics to generate approximate solutions. e

concept of information exposure was came up in [24], and an

approximation algorithm was presented to solve the problem

of nding the worst (best) information exposure path in

WSNs. In [25, 26], an approximation algorithm was suggested

by Djidjev to solve the minimum exposure-path problem and

guaranteed the network performance. Ferrari and Foderaro

[27] introduced an articial-potential approach that designed

the minimum exposure paths of multiple mobile objects

(including sensor nodes) in dynamic networks. In addition,

this approach can be used in heterogeneous wireless sensor

networks (HWSNs). e authors of [28] exploited a new

optimization algorithm, the physarum optimization, for solv-

ing the shortest path problem. is algorithm is with low

complexity and high parallelism. Liu et al. [29] applied the

percolation theory to solve the exposure-path problem with

a two-dimensional (2D) Poisson process in Internet of ings

(IoT).

Using percolation theory to nd the critical density of net-

works could date back to 1961. Gilbert [30]rstlyraisedthe

concept of continuum percolation to nd the critical density

of a Poisson point process. is model is the foundation of

wireless networks with continuum percolation. Percolation

thresholdisalsoappliedtoinvestigatetheconnectivityof

wireless networks. In [31], Penrose indicated that the critical

range for the probability of establishing overall connectivity is

close to 1, as the number of nodes goes to innity. is range

results in every node connecting to its neighbors on average.

GuptaandKumarof[32] adopted the correlation percolation

results to derive the sucient condition on communication

distance for asymptotic connectivity in wireless networks.

However, the loose lower and upper bounds on the critical

density impose restrictions on the applications of continuum-

percolation theory.

Bertin et al. [33] put forward the existence of site and

bondpercolationforbothPoissonandhard-corestationary

point processes in the Gabriel graph. Besides, the simulation

results demonstrated the critical bounds corresponding to

the existence of two paths—open sites and open bounds,

respectively. In [34], the authors determined the critical

densities of a Poisson point process in dierent classes of

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