2013 13th IEEE/ACM International Symposium on Cluster, Cloud, and Grid Computing
Empowering the invulnerability of wireless sensor networks through super wires and super nodes Xiuwen Fu Dept. of Logistics Engineering Wuhan University of Technology 430063, WuHan, P.R. China Email:
[email protected]
Wenfeng Li
Giancarlo Fortino
Dept. of Logistics Engineering Wuhan University of Technology 430063, WuHan, P.R. China Email:
[email protected]
Dept. of Electronics, Informatics and Systems(DEIS) University of Calabria 87036, Rende (CS), Italy Email:
[email protected]
invulnerability. In order to improve the performance of WFANs based on WSNs by enhancing the network invulnerability, the effect of complex theory on invulnerability is analyzed from a systematic perspective and two novel schemes are proposed in this paper. The rest of this paper is organized as follows. Section II gives a brief overview of the related work. The definition of WFAN and the main measurements of network invulnerability are proposed in Section III. Section IV discusses the performance of complex network theory in enhancing the invulnerability of networks. Section V presents a novel centrality measurement. Two schemes for invulnerability are proposed and their performances are tested by simulation in section VI. Finally conclusions are drawn and future research is briefly delineated.
Abstract—Network invulnerability is an important property of networks that operate under very likely physical attacks and failures due to operating environmental conditions. A notable example of such networks is wireless fire alarming networks (WFANs) that are strongly related to the safety of the public and to the efficiency of rescuing. WFANs based on wireless sensor networks (WSN) are gaining momentum as they considered a viable and effective solution. However, the current research on invulnerability in the WSN domain mainly focuses on the optimization of the sensor node layout in the initialized network and on routing protocols, whereas the importance of optimization of the deployed network is less explored. In this paper, we show that the invulnerability of WSNs can be improved by introducing two new elements: super wires and super nodes. Moreover, on the basis of the definition of a novel centrality measurement, we propose two layout schemes based on super wires and super nodes for enhancing network invulnerability. The simulation analysis indicates that the proposed schemes are able to enhance the invulnerability of the network with low network construction costs.
II.
The invulnerability as a property to measure how strong the network can last while facing faults or attacks, has attracted a lot of attention from many researchers in various domains. Boesch and Thomas [6] carried on a research on the invulnerability of communication network under natural or enemy damages by proposing two measurements of invulnerability using fixed cost for edges and the complete bipartite graph respectively. Fratta and Montanari [7] calculated the invulnerability of communication networks by transforming a Boolean sum of products into an equivalent form in which all terms are disjoint. Although several criterions of optimality are presented in such two papers, these methods fail to deal with the dramatic enlargement of the network scale due to high algorithm complexity. With the further development of the complex network theory, especially the discovery of small world and free scale effect, the research of the network invulnerability has achieved a higher level. Albert et al. [8] was among the first to focus on the invulnerability of Erdos and Renyi (E-R) network and the scale-free network under random and selected attacks. They found that the scale-free network shows a surprisingly high degree of tolerance against random failures and the enhancement of the failure tolerance is at the expense of the attack tolerance. Conversely, the invulnerability of E-R network against attack damage performs better than scale-free network, of which failure tolerance is not as good as scale-free network. Since then, this research result has become the central topic
Keywords—Invulnerability; Wireless sensor networks; Super wires; Super nodes; Centrality measurement.
I.
INTRODUCTION
Fire is one of the most common disasters, threatening the security of the public, which has caused serious losses of lives and properties. With the increasing wealth of the society, the potential factors causing fire are also raising dramatically. Due to the high construction cost and failure rate, the traditional wired fire-alarming systems are not able to meet the requirements of the fire monitoring in the modern society [1, 2]. Wireless sensor networks (WSNs) allows for effective and real-time distributed sensing of many type of environments. Thus, combining fire-detection technology with WSNs can avoid many drawbacks of the traditional fire-alarming networks, and such combination is currently an important research area in the domain of fire security [3, 4]. There are several challenges that arise in the design of a wireless fire alarming network (WFAN). One of the major challenges is how to keep the network working normally or extend its lifetime in extreme conditions [5]. Due to the specialization of their application context, WFANs always operate under the risk of fire attacks and fault failures, which lead to a significantly high requirement of This work has been financially supported by National Science & Technology R&D Program (2012BAJ05B07), Fundamental Research Funds for the Central Universities (2012-JL-08) and international cooperation project funded by Hubei province (2011BFA012)
978-0-7695-4996-5/13 $26.00 © 2013 IEEE DOI 10.1109/CCGrid.2013.95
RELATED WORK
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denotes the set of edges. , is the subgraph of the network , meaning that the graph is the integral part of the graph . If a link exists between every two nodes as the connected subgraph of . If the in , we define network consists of subgraphs, we define subgraphs , , , ,… , , . If as , ,…, and every node in keeps at least one link with Sink node. We define , as the effectively connected subgraph. The Invulnerability measurement based on effectively connected subgraphs is defined as follows: 1 (1) C= ω | Vi | ω∑ δ is li i =1 | V | where denotes the connected coefficient and represents the number of the subgraphs in the network . | | means the number of nodes in the subgraph . is the average length of the shortest path between any nodes in the subgraph . ⎧1 Every nodes of Vi at least has one link with Sink node δ is = ⎨ ⎩0 None of the nodes of Vi has link with Sink node if we remove nodes randomly from the network , and the connected coefficient achieves the threshold , then we can call the invulnerability value of the network based on the network connectivity [10]. The Invulnerability measurement based on the maximum subgraphs is defined as follows:
in the domain of invulnerability, and has been further researched in many different contexts. For example, Dunne et al. [9] focused on the food chain and showed that the food chain network has high sensitivity to removal high connected species. Jeong et al. [10] focused on the protein network and demonstrated that the highly connected proteins are more likely to be more important than proteins with low links to other proteins and this property of the proteins network exists in other networks commonly as well. WSNs are a major research and technological area and their invulnerability also attracted more and more concerns. Qi et al. [11] proposed a method to evaluate the importance of nodes in WSNs based on the remaining energy and to estimate the invulnerability of network by calculating the variation and average values of the network according to the importance of nodes. However, before using the evaluation method, the energy factor and contribution factor β have to be configured at first. Actually, due to different networks having various characters, it is difficult to define the exact factors and β. Lin et al. [12] proposed invulnerability measurement based on the effective connectivity which successfully considers the typical characters of WSNs such as cluster structure and convergence effect. Despite Lin et al. mentioned that the small world effect is able to improve the invulnerability of the WSN, but the related deduction or simulation was not presented in their paper. Helmy [13, 14] firstly proved that the small world effect can also be applied in the WSN by importing super wires and then testified that using small world effect to reconstruct WSN is able to improve the performance of the WSN by 70% in energysaving and energy-balancing. Ming [15], Cavalcanti [16] and Anbo [17] reconstructed WSNs from heterogeneous networks by introducing super nodes. Due to the super nodes having a better performance in memory, computing and transmitting range, the exploitation of super nodes is able to improve the connectivity and energy consumption of the network. However, the current research on complex network theory in WSN mainly focuses on the improvement of energy consumption and routing protocols, and currently involves less the effect of complex network theory in invulnerability of WSN. III.
P=
| Vmax | |V |
(2)
where denotes the coverage rate of the maximum max | |, | |, … , | | ). | | represents subgraph ( the number of nodes in the network . if we remove nodes randomly from the network , and the maximum subgraph coverage rate achieves the threshold , then the invulnerability value of the network we can call based on the maximum subgraph [17]. IV.
INVULNERABILITY ANALYSIS
This section will show the effect of complex network theory in invulnerability of WSNs by simulation. The simulation is located in a square area of 1000 1000 m where 100 wireless sensor nodes are randomly deployed. If the node is working normally, it will be labeled by the blue color. Conversely, the failed node will be marked as black. The transmitting and detecting radius of the nodes is 150m. The transmitting radius of the super nodes is 300m and detecting radius is as same as the normal node. The Sink node will locate in the center of the square and be marked as red. During the simulation, the network will be added super wires and super nodes separately to enhance the invulnerability performance of the network. The super wires are marked as red and the super nodes are marked as green. In the simulation, we don’t consider the negative impact of the signal conflicts and outside interruption (e.g. electromagnetic interference).
INVULNERABILITY MEASUREMENTS
The definition of the invulnerability seems to be different under various attack schemes. Currently, the attack schemes mainly include random attack and selected attack [18]. The random attack means that the probability of attack of the nodes in the network is uniformly distributed while the selected attack scheme indicates that the most important nodes undertake a higher attack probability. Due to the occurrence of the fire which belongs to the random nature event, the invulnerability of WFANs should be defined as survival ability under the random attack. Assuming that there is only one Sink node in the network and every node in the network knows the location of the Sink node. We use , to indicate the topology of this network where is the set of nodes and
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(a) initialized network
(b) post-failure network
(c) post-failure network with super wires
(d) post-failure network with super nodes
Figure 1. Comparison of networks under four different cases
Figure 1(a) indicates the state of the initialized network in which every node works well and keeps at least one link with the Sink node. Figure 1(b) shows the state of the network after removing 40 nodes randomly. It is obvious that the topology of the network is almost collapsed and only 19 nodes are able to keep normally connected. The remaining sensing area accounts for less than 30% of the initialized network sensing area. Figure 1(c) and Figure 1(d) show the state of the network by adding 10 super wires and 10 super nodes, respectively. Even through the network remove 40% of nodes, the network still operates well and can still maintain more than 80% sensing area. According to the initialized configuration without super wires and super nodes, the threshold is 0.5 ( 0.5 . From 100 simulations of random network topology, we can get that the invulnurability of the network with respect to network connectivity is 0.29 ( 0.29), which means the network is able to afford the loss of 29 nodes and that the invulnurability with the coverage rate of the largest branch is 0.21 ( 0.21) . It is clear to discover that the network can be destroyed easily.
However, with the increasing number of super wires and super nodes, the invulnerability is improved significantly. As shown in Figure 2, when the number of super wires is at the lower level, the improving performance of invulnerability is negligible. When the number becomes relatively higher, the effect of super wires on invulnerability is evident. As shown in Figure 3, the performance of super nodes is not so different from super wires, but is smoother. It is worth noting that when the percentage of super nodes and super wires reach 20% of the total number of nodes, the effect on invulnerability is almost saturated which requires constructor of the network need to build the network with a certain scheme. Increasing super nodes or super wires excessively will not enhance the effect on invulnerability, but will raise the budget and lower the performance of the network due to the raising of path calculation. Therefore, there is an urgent demand to develop an optimized scheme to enhance the invulnerability performance.
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Figure 2.
Performance curve of invulnerability based on super wires
Figure 4.
Typical cluster structure of WSN
TABLE I. COMPARISON OF MULTIPLE CENTRALITY MEASUREMENT
Figure 3. Performance curve of invulnerability based on super nodes
V.
CENTRALITY MEASUREMENT OF WSN
Due to the inequality characteristics of WSNs, some key nodes decide whether the entire network can operate well. To enhance the invulnerability of the network, the most effective way is to lower the centrality of the key nodes. The essence of the optimized scheme is to lower the importance of the key nodes and thus enhancing the invulnerability. In the complex network theory, we usually refer to the importance of the nodes as the centrality [18]. Different networks need various measurements to measure the centrality of the nodes. The typical centrality measurements include: degree centrality, closeness centrality, eigenvector centrality and betweeness centrality. However, being WSNs sorts of data centralized networks due to the presence of the sink node, such centrality measurements fail to indicate the different importance of the nodes in the whole network. Figure 4 shows a typical cluster topology of WSNs.
WSN betweeness centrality 1
Degree centrality
Closeness centrality
Betweeness centrality
Eigenvector centrality
2
0.23
0.565
0.615
0.59
3
0.461
0.52
0.641
0.69
0.46
4
0.461
0.52
0.641
0.69
0.46
5
0.069
0.351
0
0.255
0
6
0.069
0.351
0
0.255
0
7
0.069
0.351
0
0.255
0
8
0.069
0.351
0
0.255
0
9
0.069
0.351
0
0.255
0
10
0.069
0.351
0
0.255
0
11
0.069
0.351
0
0.255
0
12
0.069
0.351
0
0.255
0
13
0.069
0.351
0
0.255
0
14
0.069
0.351
0
0.255
0
15
0.069
0.351
0
0.255
0
Node
The degree centrality as the earliest and simplest centrality measurement is defined as the number of ties a node has and this centrality is always interpreted in term of the direct influence of a node in static network. The formula to calculate degree centrality in a network with nodes is shown below [19, 20]:
Cd ( x ) =
d ( x) n −1
(3)
where represents the degree centrality of node and denotes the number of ties node has. The closeness centrality is a centrality measurement which is used to measure how fast a node will take to spread information to the entire network. As a more valid way to
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indicate the breakdown of the node will not influence other nodes’ work.
detect the centrality structure of the network, it is widely applied.
⎡ n ⎤ Cn ( x) = (n − 1) ⎢ ∑ d xy ⎥ ⎣ y =1 ⎦
−1
(4)
where represents the closeness centrality of node denotes the distance from node to node which and also can be defined as the least hops from node to node . The eigenvector centrality is the centrality measurement used to reflect the intimate degree between specified nodes and high-degree nodes in the network. For a given network whose adjacency matrix is , if a 1 , link exists between vertex and vertex , otherwise 0. n
Ce ( x ) = λ −1 ∑ aij e j
(a)
where and represent the eigenvector centrality of the node and eigenvalues of matrix respectively and is the unit vector. The betweenness centrality [21] is a measure of a node's centrality in a network equal to the number of shortest paths from all vertices to all others that pass through that node. The betweeness centrality of a node is given by the expression:
σ st (v) s ≠ v ≠t σ st
∑
(6)
is the total number of shortest paths from node where to node and is the number of those paths that pass through . From Table 1, it can be noticed that nodes 3 and 4 are lower than node 2, according to every centrality measurement except closeness centrality. However, if the node 2 stops working, the entire network will collapse while 50% of the nodes in the network can still work well when facing the failure of node 3 and 4 separately. Despite the closeness of the node 3 and 4, they are slightly lower than node 2, but actually, the node 2 is far more important than nodes 3 and 4. Therefore, we propose a novel centrality measurement, named WSN betweeness centrality, which is defined as follows:
Cc ( x) =
∑ g ( x) / g k
k∈v
n−2
(c)
Figure 5(a) demonstrates the distribution of WSN betweeness centrality of the network in Figure 1(a). In general, the betweenness centrality of the nodes closed to the Sink node is much higher than any other nodes. And the distribution of WSN betweeness centrality is extremely nonuniform, which indicates the network has a poor invulnerability. Figure 5(b) indicates the distribution of WSN betweeness centrality of the network with random deployment of 10 super wires. The centrality of the network decrease dramatically. Figure 5(c) indicates the distribution of WSN betweeness centrality of the network with adding 10 super nodes, the invulnerability of the network is improved a lot due to the uniform distribution of centrality. Figure 5 testifies the effect of super wires and super nodes on invulnerability again by simulating their contribution on uniform distribution of WSN betweeness centrality in the network. Aiming to better explore the effects of super wires and super nodes, a further analysis are carried on next.
(5)
j =1
Cb ( x) =
(b)
Figure 5. (a) centrality distribution of the intialized network; (b) centrality distribution of the intialized network with super wires; (c) centrality distribution of the intialized network with super nodes;
(a)
(b)
(c)
(d)
(e)
(f)
k
(7)
where is the number of the shortest paths from node to Sink node, which pass through the node . is the number of the shortest paths from node to Sink node. Among the network with ( 2 ) nodes, the extreme situation is every shortest path from any other nodes except node to Sink node pass through the node , while the WSN betweeness centrality is 1. From the Figure 4, the WSN betweeness exactly reflects the centrality of the network. The centrality of node 2 is as twice times as that of node 3 and 4. The centrality of other nodes is 0, which
Figure 6. The centrality distribution by deploying super nodes from 10 to 26. (a) 10 super nodes; (b) 14 super nodes; (c) 18 super nodes; (e) 22 super nodes; (f) 24 super nodes; (g) 26 super nodes;
From Figure 6, although it is easy to find that the distribution of WSN betweeness centrality has become more uniform with the increasing number of super nodes, there still exists some interesting phenomenon worthy noticing. At the initial stage, the effect of adding super nodes on
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super nodes are required according to the network with deployment of super nodes. Through the above analysis of performance of super wires and super nodes on the uniform distribution of network centrality, the super nodes and super wires has been proved to be effective ways to improve the invulnerability of the network. Nevertheless, both of them have their own drawbacks. Although from the Figure 5, 6 and 7, super nodes performs better than super wires, the introduction of the super nodes will transform the network with same kinds of nodes into a heterogeneous network, which thus increases the complexity of the routing mechanism and system maintenance. Moreover, compared with general nodes, the cost of super nodes is much higher, thus leading to dramatic increase of the construction cost of the network. When it comes to super wires, it also has some shortcomings that merit attention. By contrast with the super nodes of which data delivery relies on wireless transmission, super wires transmit data depending on wires which is also under the risk of fire attack. Thus when fire occurs, the network with super wires could be faultier. Therefore the mixture of super wires and super nodes might help us balance trade-off among factors such as system complexity, construction cost and network failure. As in most cases, the network constructors are more preferred to select one invulnerability scheme to guarantee the simplicity of the system and the proportion of super wires and super nodes is different according to different application scenarios, here in this paper, we only put emphasis on the effect of super wires and super nodes on centrality distribution and do not put a further analysis of their mixed effect.
distribution of WSN betweeness centrality is more obvious, the tendency of which is also similar to the results shown in Figure 3 demonstrating the effect of super nodes on network invulnerability. From the Figure 3, it can be noted that when the proportion of super nodes reaches 20% of the total number of nodes, the effect on invulnerability is almost saturated. We can also find such similar result in the Figure 6. Before the number of super nodes reaches 20 in the network, the effect of super nodes on improving centrality distribution is rather significant, however, when the super nodes outnumber 20 (counting 20% of total number of network), the change of distribution becomes stable. Besides that, when the centrality distribution achieves relatively stable, the deploying of the super nodes will lead to the emergence of some new points with relatively higher centrality and the location of these nodes changes dramatically with the latest deployment of super nodes.
(a)
(b)
(c)
(d)
(e)
(f)
VI.
LAYOUT SCHEMES FOR INVULNERABILITY
In this section, two layout schemes for invulnerability are proposed, based on the WSN betweeness centrality. The roles of nodes playing in the network are mainly determined by the ability of nodes in controlling the information-flow of the network. The way to reduce the centrality of key nodes is to make the link passing through key nodes replaceable and thus improving the network invulnerability. Therefore, the essence of the two proposed layout schemes is to lower the impact of key nodes on information-flow of the network through building an alternative link between the upstream and downstream of key nodes. In order to illustrate the proposed schemes briefly and clearly, the description of network , is used here again and the definition of upstream and downstream of nodes is listed as below:
Figure 7. The centrality distribution by deploying super wires from 10 to 34. (a) 10 super nodes; (b) 16 super nodes; (c) 22 super nodes; (e) 28 super nodes; (f) 30 super nodes; (g) 34 super nodes;
As shown in Figure 7 which demonstrates the distribution of WSN betweeness centrality, the centrality distribution is able to be improved significantly by introducing super wires into the network. Despite the distribution of high centrality fields tends to be similar between adding super wires and super nodes when the number reaches a certain level, the network with added super wires still exhibits some evident differences in comparison with the centrality distribution of network with super nodes. From the perspective of shape of highcentrality fields, the network with deploying super nodes tends to be scattered, while the network with super wires demonstrates more centralized tendency that most of areas with high centrality locate in the geographical center of the network. Moreover, compared with super nodes, the effect of super wires on centrality distribution is less obvious, which the network requires more than 28 super wires to reach the optimistic centrality distribution while less than 24
⎧Vd ( n) The set of nodes belonging to the shortest paths to ⎪ Sink node passing through node n ( excluding node n ) ⎪ ⎨ V ( n ) The set of nodes which is passed through on the shortest ⎪ u ⎪ path from node n to Sink node ( excluding node n ) ⎩
A. layout scheme based on super wires
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order to testify that proposed scheme can be applied widely, the transmitting radius of the super nodes is as twice time as the normal nodes. And the length of the super wires cannot go beyond 20m. Aiming to better illustrate how super wires and super nodes work, the schemed deployment of super wires and super nodes is shown in Figure 8, where super wires and super nodes are colored as red points and blue wires respectively.
Step1: get the node whose WSN betweenness centrality is the largest among the set V. The related rule that should follow is shown as below: max which is the maximum, with Step2: get the nodes . respect to WSN betweeness centrality among the set The related rule that should follow is shown as below: max Step3: get the node which is the minimum, according to WSN betweeness centrality among the set , and the related rule that should follow is shown as below: min ,
is the set of super wires that should be built.
B. Layout scheme based on super nodes Step1: get the node whose WSN betweeness centrality is the largest among the set V, and the related rule that should follow is shown as below: max
Figure 8. Layout of the office place
, which is the set of Step2: get the nodes set is 1, and the related rule nodes whose distance from that , should follow is shown as below: , |hop , x 1 which is the set of Step3: get the nodes set nodes whose shortest path pass through . Through the and comparison between , , get the set which is the intersection set between and . Step4: get the node which is the node whose WSN betweeness centrality is the largest among the set , and the related rule that should follow is shown as below: max is the super node. VII. CASE STUDY
Figure 9. Performance comparison between random depolyment and schemed deloyment based on super wires
In order to illustrate the effect of the proposed schemes on enhancing invulnerability, an experimental scenario concerning an indoor environment is analyzed in this section. The goal is to evaluate the performance of super wires and super nodes when the deployed network encounters issues such as node failure or running-out of the battery. For indoor fire-alarming network, the greatest threat is the contrived damage or poor maintenance instead of fire attack as the frequency of the man-made damage is much higher. Thus, we select a real fire-alarming network deployed in an office place under random attack in order to evaluate the performance of the super wires and super nodes on improving the invulnerability of the network facing node-failure and wearing-out of the battery. As shown in Figure 8, the indoor scenario is a layout of an actual office place with square 1000 m2. The office place is divided into a large-size public zone and 13 small-size offices. The WFAN in the office place is consisted of 55 wireless fire-alarming nodes. The detecting area of the node is 20m2. The transmitting radius of the node is 30-35 m. In
Figure 10. Performance comparison between random depolyment and schemed deloyment based on super nodes
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[3]
As shown in Figure 9 and Figure 10, the effect of deployment of super nodes and super wires using the proposed schemes is much better than the random deployment of super nodes and super wires. Since the schemes are based on the knowledge of centrality of the entire network, the lifting effect of the invulnerability is more evident at the beginning of deployment. With the increasing number of super wires, the effect curve is becoming gentle. Therefore, the maximum effect on enhancing invulnerability can be achieved with less super wires. Moreover, when super wires achieve the 15% of percentage of the sum nodes of networks, the improvement of invulnerability achieve upper limit. Through the verification of the scenario, we can draw a conclusion that the proposed layout schemes are able to enhance the performance of invulnerability of the network while maintaining a lower construction cost.
[4]
[5]
[6] [7]
[8] [9]
[10]
VIII. CONCLUSION
[11]
This paper has firstly illustrated the importance of invulnerability in WFANs and proposed the definition of the invulnerability of WFANs. By importing super wires and super nodes, the network can be reconstructed into heterogeneous networks with small world effect of which invulnerability can be improved a lot. But the random deployment of super wires and super nodes cannot achieve optimal. Therefore, a novel centrality measurement is proposed, which can reflect the centrality of the network exactly and based on the proposed centrality measurement, two deployment schemes for invulnerability of WFANs are proposed. By simulation based on the actual instance, two proposed schemes are demonstrated to enhance the invulnerability of WFANs with low construction costs. There is no doubt that with the increasing number of super wires and super nodes deployed in network, the structure of network becomes more complicated which requires more efficient routing algorithms. Especially in some extreme condition, the routing algorithm is required to fit the dynamic variation of the topology of the network. Besides that, the combined effect of super wires and super nodes are not deeply researched in this paper. Since super nodes and super wires both have their own advantages, how to maximize the effect of super wires and super nodes by mixing using them is also worthy further research. We plan to address these issues in our future work.
[12]
[13] [14]
[15]
[16]
[17]
[18] [19] [20] [21]
REFERENCES [1]
[2]
D. M. Doolin, and N. Sitar, Wireless sensors for wildfire monitoring, SPIE Symposium on Smart Structures & Materials/NDE 2005, March 2005. Martinez de Dios et al. Computer vision techniques for forest fire perception. Image and Vision Computing, 2008, 26( 4).
568
Son. B, Her. Y., Kim. J. A design and implementation of forest-fires surveillance system based on wireless sensor networks for South Korea Mountains. IJCSNS 2006, 6, 124-130. S.W. Taylor, M.E. Alexander, “Science, technology, and human factors in fire danger rating: the Canadian Experience”, International Journal of Wildland Fire, 2006, 15, pp121-135. Kewei Sha, Weisong Shi, Watkins, O. Wayne State Univ., Detroit, MI; Using Wireless Sensor Networks for Fire Rescue Applications: Requirements and Challenges, IEEE International Conference on Electro/information Technology, 2006. 239-244. Boesch F, Thomas R. On graphs of invulnerable communication nets [J]. Circuit Theory, 1970, 17(2): 183-192. Fratta L, Montanari U. A Boolean algebra method for computing the terminal reliability in a communication network. Circuit Theory, 1973, 20(3): 203-211. Albert R, Jeong H, Barabási A L. Error and attack tolerance of complex networks. Nature，2000,406: 378-382. Dunne J A, Williams R J, Martinez N D. Network structure and biodiversity loss in food webs: robustness increases with connection. Ecology Letters, 2002, 5: 558-567. Jeong H, Mason S, Barabsi A-L, et al. Lethality and centrality in protein networks. Nature, 2001, 411: 41-42. Qi Xiao-gang, Zhang Cheng-cai, Liu Li-fang. Study on node importance and network invulnerability analysis of wireless sensor network. Systems Engineering-Theory &Practice, 2011, 31(2): 34-37. Lin Li-wei, Xu Li, Ye Xiu-cai. A Novel Method and I-ts Simulation to Evaluate the Invulnerability of Wireless Sensor Networks. Computer Systems & Application ,2010,19(4):32-36. Helmy A. Small worlds in wireless networks . IEEE Communications Letters, 2003, 7(10): 490-492. Helmy A. Analysis of wired short cuts in wireless sensor networks. The IEEE/ACS Int Conf on Pervasive Services. Washington DC, 2004: 167-176. Liu Ming. Approach to construction of wireless sensor networks with small world effect. Electronic Measurement Technology, 2007, 30(4): 37-40. Cavalcanti D. Exploiting the small-world effect to increase connectivity in wireless ad hoc networks. Int Conf on Telecommunications. Fortaleza, 2004: 388-393. Meng Anbo, Chen peng. Construction to heterogeneous sensor networks based on effect of small world. Computer & Digital Engineering, 2008, 36(9): 98-100. Wu Jun,Tan Yue-jin. Study on measure of complex network invulnerability . Journal of Systems Engineering,2005, 20(2):128-131. M. Newman. A measure of betweenness centrality based on random walks. Social Networks, 2005, 27(1):39–54. Wasserman S, Faust K. Social Network Analysis: Methods and Applications . New York: Cambridge University Press, 1994. Freeman L C. Centrality in social networks: conceptual clarification. Social Networks, 1979, (1): 215-239.
