Dynamics Nature and Link Prediction Methods in ... - Semantic Scholar

Dynamics Nature and Link Prediction Methods in Opportunistic Networks Yin Li, Xuebing Zhao, Hao Tang, Qi Wang College of Software Engineering Southeast University Nanjing, China [email protected], [email protected], [email protected], [email protected]

Abstract—With the increasing popularization of low-cost smart mobile devices, which have the capability of short-range wireless communication, opportunistic networks aimed to meet different requirements start to put into practice. However, because of the mobility of nodes, links in opportunistic networks is intermittent and dynamic, which results in the problems of long delay time and low success rate of delivery. And these problems limit the further development of opportunistic networks. To solve these problems, this paper proposes a solution framework based on prediction, explores potential methods that are applicable to opportunistic networks and compares their performance and suitable application model.

I.

OPPORTUNISTIC NETWORK AND ITS DYNAMICS

Opportunistic Network (OppNets) [1] is a new network frame developing from Ad hoc networks. It can transfer the packets by hops while the nodes moving around and finally reaching the destination node on condition of a split network. Contact refers to a connection between the nodes. When the nodes (for instance, a vehicle equipped with 802.11p communication device or a mobile smartphone user) get into the communication domain of each other, then the link is established and the communication occurs. When leaving the communication domain, the link and the communication are disrupted. In opportunity networks, contact is opportunistic rather than deterministic. Because of the mobility, the end-toend link is no longer reliable, which makes traditional routing ineffective. Opportunistic networks perform a store-carry-forward model to carry services by multiple hops [1]. In Fig. 1: If the current node fails to obtain the next hop leading to destination, it stores the message and waits for forwarding opportunity while moving around. As shown in Fig. 1, at the time of t1, there is no direct path from the source node S to the destination node D. So node S delivers the message to node 3, and node 3 stores and carries the message till the time of t2 then deliver the message to the node 4. Finally, until time of t3, node 4 and the destination node D move to the same communication domain and the message is transferred successfully.

SanFeng Zhang† Key Laboratory of Computer Network and Information Integration in Southeast University, Ministry of Education Southeast University Nanjing, China [email protected]

Fig. 1. Store-carry-forward model in opportunistic networks

Opportunistic network is low-cost and easy to deploy. These characteristics make it a basic network frame in Vehicular Ad Hoc Network (VANET), mobile data offloading [2][3][4], cooperative content sharing [5][6] ， mobile computing sharing [7][8][9], etc. With the frame of opportunistic networks, message delivery, content distribution, resource sharing and other functions can be realized regardless of the infrastructures or just in need of a small number of infrastructures in the remote highways, urban transport, mobile social networking and other scenes. In conclusion, these opportunistic networks application systems have plentiful prospects. Their performance and the user experience are largely dependent on the network transmission service provided by opportunistic networks.

Fig. 2. Intercontact time of nodes

assumption, we believe that it is possible to predict the dynamic changes of links in opportunistic networks. We propose a prediction-based solution framework in opportunistic networks as shown in Fig. 4.

Fig. 3. Duration of links

However, there are some challenging issues remaining to be solved in opportunistic networks with a special network frame. And the dynamics of the network topology is the most important issue among them. In order to save energy, the wireless transceiver will be turned on and off. These operations and the movement of nodes will result in the adjacency matrix of nodes changing with time dynamically. What is shown in Fig. 2 is the statistics of average intercontact interval of nodes in Netsense dataset [10]. This dataset is a collection of the bluetooth log and WiFi connection log of two hundred students in Notre Dame University. As shown in the figure, the average intercontact interval is about 1000 minutes, nearly 16 hours. And they vary greatly from different nodes. Thirty percent of the nodes pairs have a intercontact interval no more than tens of minutes, percent of the nodes pairs have an intercontact interval over a week. And in Fig. 3, forty percent of nodes pairs have a link duration no more than one minute. The dynamics make it difficult to determine a forwarding path. Therefore, in order to improve the performance of transmission, we can use multiple copies of the message. Besides, we can choose suitable next hop according to the criteria of transmission utility [11]. But there are still some problems: (1) The success rate of delivery is low. Messages are discarded while transferring because of exceeding lifetime or buffer overflow. The success rate of delivery is 50% normally[1] . (2) The delay of delivery is long. Because of the dynamics, the store-carry is aimless. It may take hours or days to successfully deliver the message. (3) Multiple copies store and transfer in the network is bound to take a lot of storage space and consume lots of energy. (4) Due to the lack of realtime in network, the arrival of network services is unknown and the waiting time is unpredictable, which significantly affect the user experience. The key to solving these problems is to grasp the law of dynamic changes of a single node, adjacent nodes, and the topology of the entire network, and alleviate the problems caused by the dynamics using prediction method. In many opportunistic networks, the movement of nodes and the contacts between nodes is a reflection of people's daily movements and activities [12]. As a Chinese proverb says," Go to bed with the lamb, and rise with the lark." Individual activities always follow a routine. Whom you are going to meet in the next period of time is largely related to your social relationship or the other social features. Based on this

Fig. 4. Prediction-based solution framework to the dynamic problem in opportunistic networks

II.

ISSUES OF LINK PREDICTION IN OPPORTUNISTIC NETWORKS

According to the method shown in Fig. 5，we divide the topology of entire network, which is changing with the time, into snapshots. And we construct an adjacency matrix E representing the contacting frequency of nodes during each timestep of equal length. Then we get a series of snapshots represented by (G1, G2, G3,…,Gt). At last, link prediction is defined as: Given a series of snapshots (G1, G2, G3, ..., Gt), and get the network topology snapshot Gt+1 by studying the changing law of historic snapshots. t0

t1

t2

Fig. 5. Network snapshots

There are three evaluation indexes for traditional link prediction typically: AUC, Precision and Ranking Score. These three indexes evaluate the prediction accuracy from different perspectives. AUC evaluate the pros and cons of the prediction from the overall results of the prediction sort. AUC randomly choose a present edge and an absent edge from the testing set Gt+1 and compare them. If the value of present edges in Gt+1 is bigger than that of absent edges, add 1 point, and if they are equal, then add 0.5 points, otherwise add 0 points. Do the compare n times. If we add 1 points n ' times and add 0.5 points n'' times, the AUC is:

AUC =

n '+ 0.5n " n

(1)

In this formula, AUC = 0.5 is the reference line, which represents the randomly generated AUC values. When the AUC ratio is close to 1, it means that the prediction accuracy of

the algorithm is very high. Precision is defined as accuracy ratio of the first n edges in the prediction:

Pr ecision =

m n

(2)

In the formula, m represents the number of edges predicted accurately. Precision mainly concerns about the prediction accuracy of first n edges. The greater the precision is, the higher is the prediction accuracy. In our follow-up experiments of link prediction, we mainly use Precision as the evaluation of link prediction. Ranking Score mainly concerns about the rank of present edges in Gt+1 in the final ranking. The system Ranking Score of Gt+1 is:

RS =

ri 1 p ∑ | E | i∈E p | H |

(3)

In the formula, H is the set of unknown edges, ri represents the rank of the unknown edge i. This method evaluates the link prediction result according to the final sort. Although the link prediction ability of each prediction algorithm can be evaluated accurately, it does not have an extensive significance in practice. Therefore, we barely use this method. III.

METHODS OF LINK PREDICTION IN OPPORTUNISTIC NETWORKS

A. Context-based link prediction In the early design of routing in opportunistic networks, routing features, which do not change over time are used to indicate the probability of next link establishment, such as the average contact time, contact frequency, etc. There is a prediction method based on the number of contact in history. The contact in history is more, the probability of meeting that node in the next period of time is higher. If two nodes haven’t meet for a long time, the probability of a link establishment between them will age as time goes by. The predicted values are also dynamically maintained, updated as time goes by. In the Prophet [13] routing algorithm, the probability of link establishment is also evaluated by the contact of nodes. If two nodes meet, update the probability of link establishment with a higher value. If two nodes haven’t meet for a long time, the probability will age. Using average contact intervals in history is also a simple and effective link prediction method. Each node in the network dynamically maintains the average contact interval with other nodes. The smaller the interval is, the more frequently they meet, and the higher is the probability of a link establishment in the future. According to the work of Liu, Cong et al. [14], the average contact interval of nodes obeys the exponential distribution, the relationship between the probability of two nodes establishing a link in next timestep and the average contact interval is: Pij = 1 − exp( −U / M ij ) . In the formula,

Pij is the probability of the link establishment. U is the length of timestep.

M ij is the average contact interval. We can also

estimate the probability of contact by the length of time since the pair of nodes met last time. The duration of the link is also an effective measurement. The probability of the link between node i and node j is: Pij = Tconn / Tw . Tw is the length of timestep， Tconn is the duration of link in the timestep. The current position of nodes and direction of movement can also be used to predict the links in the next period of time [15]. Lindgren et al. [13] propose a method based on the motion vector to estimate the probability of contact in Vehicular Ad Hoc network(VANET). Assuming in the Vehicular Ad Hoc network, each vehicle is equipped with a GPS device, and you can get the current position and direction of movement of the vehicle in real time. The vehicle's current direction vector and the vector between the current position to the target vehicle will form an angle. Because the vehicle is moving along the road rather than move randomly, the probability of contacts can be estimated by the size of the angle. Besides the above parameters used in context-based prediction, there are the energy of nodes, speed of movement, density and attributes of nodes, etc. This method of link prediction is relatively simple and practical. And it is not difficult to achieve. But there are lots of limits and requirements of knowledge about the local or global network. Some assumptions are too idealistic, which are not suitable for the real network. So it has some limitations. B. Link prediction in opportunistic networks based on time evolving graph model In opportunistic networks, topology is changing dynamically. Link prediction based on time evolving graph model uses the evolving graph in dynamic network to describe the evolution of topology as time goes by. It estimates the probability of link from an evolutionary point of view. Cai, Qing-Song et al. [16] proposed an evolving graph model based on independent edge evolution. It uses Markov chain and the process of lifetime to describe the evolving process’s relevance to time. And finally, estimate the rate of birth and death using Laplace rule of succession. This model proposes that the evolution of any link is independent of the other links. The appearances and disappearances of the links are only time-related. The evolution of links obeys Markov properties, and their lifetime can be described by Markov chains. Fig. 6 is a state transition diagram. b(e) indicates the probability that the link e is absent at the time t and present at time t+1. d(e) indicates the probability that the link e is present at the time t and absent at time t+1. b (e) and d (e) indicates the probability of the birth and death of the link e. The complexity of this prediction algorithm is pretty high. The maintenance of evolving graph and the computation of probability cost a lot. So it is not suitable for large-scale network. And Markov chain ignores the social features and historical regularity of nodes in opportunistic networks, which results in some deficiencies.

Fig. 6. The Markov chains of link evolution

C. Link prediction based on time series analysis Link prediction based on time series analysis [17] is to compile and analyze the time series, then perform analogy or extension according to the information reflected by the time series, including the developing process, direction and trends. Ultimately, this method can predict what level can be reached in the next period of time. In a dynamic opportunistic network, the link of a pair of nodes changes over time, which can be observed. Using time series analysis to realize prediction, the first step is to collect the statistics of links of target nodes in history. Then obtain the variable sequence indicating whether there is a link and the quality of the link; Then create a mathematical model, show the changing law of time series, and calculate the predicted value of the time series in the future. There are a variety of ways to describe the changing law of the time series: The arithmetic average method uses the statistics of several periods as the observation value to calculate the arithmetic average as the predicted value of next period of time. Weighted time series average method is to weight the historical data of each period by the influence of the length of time. Then calculate the average as the predicted value. Simple moving average method is to calculate the arithmetic average of several periods successively as the predicted value in next period of time. Weighted moving average method is to calculate the simple moving average by weighting. When the weights are determined, weights of short-term observations should be higher, and the weights of long-term observations should be lower. Exponential smoothing method is to use the actual value in last period and the predicted value in historical statistics to realize prediction by exponential weighted method. For the link prediction in opportunistic networks using time series analysis model, the biggest problem is to fully consider the social attributes of nodes, the given date, place, other link information of nodes, etc. D. Link prediction based on spatio-temporal periodic behavior mining algorithm Spatio-temporal periodic behavior mining can be defined as a process that mining implicit, unknown but potentially useful information and knowledge from the spatio-temporal data, which is massive, high-dimensional, high-noise , nonlinear , etc. For dynamic networks, the main task is to dig the spatiotemporal periodic pattern of the tracks of nodes. Hu, Yu-Peng et al. [18] proposed a spatiot-emporal periodic behavior mining algorithm based on level bipartite graph. It is

based on the data of social network behavior, which have dual relevance in time and space, such as people would periodically go to a particular space in a particular time to participate in an activity. This algorithm can use people’s behavior habits and moving tracks to divide the data of the dynamic social network into time slices. Then transform the entire social networks into a mode binary tree and access to the closed periodic space subsets representing the spatio-temporal periodic behavior mode. Any closed periodic space subset can reflect the internal spatio-temporal relevance of a group. When predicting, match the subsets of the target pair of nodes, and realize link prediction according to the time. This algorithm is relatively complex and difficult to implement. Meanwhile, the time complexity and space complexity of this mining algorithm are pretty high, especially in the case of a large-scale networks with many historical information, where fast search and matching is impossible, and the efficiency is low. E. Link prediction based on complex networks Complex networks consist of a large number of nodes and the complex relationships among these nodes. It fully or partly has the properties of self-organizing, self-similar, small-world and scale-free. Link prediction in complex networks [19] refers to predict the probability of link establishment between two nodes, who do not have a link currently, by the known information of network structure. Opportunistic networks are consistent with the statistical properties of complex networks, so we can use the method of complex networks for link prediction in opportunistic networks. F. Link prediction based on similarit Link prediction based on similarity [20] refers to predict the probability of links by the similarity between nodes. Its premise is that the greater the similarity of the two nodes is, the greater is the possibility of establishing a link between the two nodes. There are a number of ways for the description of the similarity between nodes. The easiest way is to use the attributes of the nodes, such as eigenvectors. The more similar the attributes of nodes are, the greater is the similarity. If two people have the same age, gender, occupation, interests, etc. They must be very similar. The premise of using the attributes of nodes for link prediction is that the edges themselves in networks represent the similarity. TableⅠlists the definitions of some major similarity index, Γ( x) is the set of neighbors of node x. k ( x) =| Γ( x) | is the degree of node x. The simplest similarity indexes is the common neighbors. Namely, the more common neighbors the two nodes have, the more they are inclined to establish a link. The indexes in the table drive from common neighbors with some difference of variable perspectives.

TABLE I.

Name

DEFINITION OF SIMILARITY INDEX

Definition

Common neighbors(CN)

sxy = Γ( x) I Γ( y)

Salton index

sxy =

Jaccard index

sxy =

Sorenson index

sxy =

Hub promoted index (HPI)

Name

sxy =

Γ( x) I Γ( y ) k ( x) × k ( y )

attachment index(PA)

2 Γ( x ) I Γ( y )

Adamic-Adar

k ( x) + k ( y )

index(AA)

Γ( x ) I Γ( y )

Resource allocation

min{k ( x), k ( y )}

index(RA)

p(Aij = 1| M ) = Qαβ of

connection between node i in group and node j in group α . The reliability of this block model for the target network is： l

r −lαβ

p( Aij | M ) = ∏ Qαβαβ (1 − Qαβ ) αβ

(4)

α ≤β

In the formula, A is the adjacency matrix of the target network.

lαβ is the number of connected links between the

node in group network.

α

and the node in group

β

in the original

rαβ is the total number of the possible connections

of nodes in group

α

and the nodes in group

β .As shown in

the formula, this method is consistent with the formula of hierarchy model. The optimal probability is

*

Qαβ = lαβ / rαβ .

Generate all possible block model M using the above method.

max{k ( x), k ( y )}

sxy =

LHN-I index

Γ( x) U Γ( y )

Γ( x) I Γ( y )

sxy =

(HDI)

Preferential

Thereby we establish a block model M. According to the block model, we can get the probability

Hub depressed index

Γ( x) I Γ( y )

G. Link prediction based on maximum likelihood method Stochastic block model(SBM) [21] is a method based on maximum likelihood. Its basic idea is to divide the nodes in networks into groups using the modularity characteristic of networks. Whether there is a connected link between the two nodes or not is determined by the groups they belong to. If the target network has N nodes, in order to use SBM to predict the link, at first we need to divide the N nodes into groups, and then assigned a probability of connection Qαβ to each group.

Definition

Γ( x ) I Γ( y ) k ( x) × k ( y )

sxy = k ( x) × k ( y ) sxy =

1 z∈Γ ( x ) I Γ ( y ) lg k ( z )

sxy =

∑

1 k ( z) z∈Γ ( x ) I Γ ( y )

∑

Ultimately, the credibility of the connection between node i and node j is:

RijL = p( Aij = 1| A) =

∫

Ω

p( Aij =1 | M ) p( A | M ) p(M )dM

∫

Ω

p( A | M ') p( M ')dM '

(5)

In the formula, Ω is the set of all possible block models (We do not need to consider all the model in practical computation). In order to simplify the calculation, p (M) may be set to a constant. The higher the credibility is, the higher is the probability of a connection. Stochastic block model can not only predict the missing edge, it can also determine the wrong edge by the credibility, such as the misconceptions of the interaction between proteins. Stochastic block model performed better than the hierarchical model on average, especially when predicting the error edges. But they both have the problem of high computing time complexity. Link prediction based on complex networks is actually a reflection of static statistics of the known links in history, rather than reflecting the law of topology evolving over time. It also lacks the consideration about the given date, place and other known conditions. We need to combine some methods of the time series analysis and the parameter estimation to improve the application efficiency of link prediction based on complex networks. IV.

EXPERIMENTS OF DIFFERENT PREDICTION METHODS

A. Trace datasets We use two trace datasets of mobile users to simulate the mobile nodes in OppNets. They are UCSD WiFi dataset and Southeast university of China (SEU) WiFi dataset. UCSD WiFi dataset records the association between 272 users and 514

access points on campus. The information is updated every 20 seconds for all APs that it could sense across all frequencies-not just the AP the wireless card was associated with at the time. The data is collected during an 11 week trace period from 9/22/2002 00:00:00 to 12/8/2002 00:00:00. SEU Dataset is collected by the staff of SEU internet center, consisting of 17512 users and 661 Aps in the teaching building, library and college’s office buildings from 11/15/2013 00:00:00 to 11/22/2013 00:00:00. The form of records is similar to that in UCSD dataset, but it has a larger number of users and APs.

contact in the future, 24.4% of them are predicted negative in periodic pairs set, and 39.6% of them are predicted negative in non-periodic pairs set. In total, 64% of links still haven’t been detected.

 

In preprocessing, we extract contact data of the nodes from the traces. Considering fault-tolerance, if there are two records with the same node and AP within two minutes, they are subsumed. Then, if two nodes associate with one AP at same time, we regard it as a contact. Considering the lack of association duration in UCSD dataset, if two nodes associate with one AP in 10 seconds, we regard it as a contact. We choose 10s as the interval by experiments. Because that experiment results show that the prediction accuracy won’t change a lot when increasing this interval. It means that the increase will only bring redundancy. Besides, we also get rid of the noise data at PM12:00~AM8:00 which is too sparse.

 

B. Evaluation indicators Some evaluation indicators are commonly used to evaluate the prediction performance: precision =

recall =

 

tp tp + fp

 

tp tp + fn

F − measure = 2 ×

Fig. 7. Comparison of preidiciton methods.

precision × recall . precision + recall

In simple terms, high precision means that an algorithm returned substantially more relevant results than irrelevant, while high recall means that an algorithm returned most of the relevant results.

V.

IMPLEMENTATION OF LINK PREDICTION IN OPPORTUNISTIC NETWORKS

Because that the data is very sparse. The correction ratio of all nodes is pretty high, because most of them are tn (true negative). So we don’t focus on this indicator. In contact prediction, we choose precision to represent the correction ratio of pair which is predicted to contact. And recall represents the correction ratio of pair which will exactly contact. F-measure is a synthesis of precision and recall. C. Experiment results We compare the performance of different prediction methods we discussed. In Fig.7, the experiment results show that PSE outperforms the others in aspect of precision, recall and F-measure. But PSE has a main disadvantage. When the dataset show non-periodic contact pattern or the duration of training set is too short to form a periodic pattern, most pairs are predicted negative, namely no contact in the future. In terms of delivery in networks, this negative prediction leads to huge waste of throughput. For example, in our on-campus datasets, non-periodic pairs are over 90 percent of all pairs. As shown in the last graph of Fig.7, among all pairs who have a

Fig. 8. The way to implement the link prediciton

A. Centralized mode and distributed mode Since the existing smart mobile devices generally have the capability to access 3G/4G wireless mobile network, it is feasible to transfer limited amount of data of the topology information and prediction results through the 3G/4G network. The mobile terminals only need to maintain a small amount of short-term topology information and some long-term results of statistics and then interact with the server regularly. The server maintains a large database of topology information and then performs data processing and predicting computation periodically. The mobile terminals perform opportunistic transmission via the low-cost WiFi Direct or the Bluetooth. The transmission decisions are assisted by the prediction. Under a limited circumstance, we can use a fully distributed mode. At this point, the mobile terminals need to maintain a large-scale knowledge base, and interact their topology information in addition to the message when contacting each other. So, eventually, each node is able to maintain a relatively complete knowledge base. In this case, we need to assess some factors’ influence to the performance of prediction, including the completeness of the topology information and the real-time degree. B. Online and Offline For the prediction with a requirement of real-time and dynamic, online implementation method is needed. But the laws of nodes’ movement is usually stable, and the dynamics of nodes set is not very intense. Most applications of prediction can rely on updating information and feedback of prediction periodically. The specific mode of operation and the frequency of period remain to be evaluated in the research of specific link prediction algorithm.

[5]

[6]

[7]

[8] [9]

[10]

[11]

[12]

[13]

[14]

[15]

VI. CONCLUSION In this paper, we analyze the dynamics problems in opportunistic networks and propose a solution framework based on prediction. We focus on the possible methods of link prediction and their implementations. Then we evaluate and compare the advantages and disadvantages of each method. REFERENCES [1]

[2]

[3]

[4]

Spyropoulos, Thrasyvoulos, Konstantinos Psounis, and Cauligi S. Raghavendra. "Spray and wait: an efficient routing scheme for intermittently connected mobile networks." In Proceedings of the 2005 ACM SIGCOMM workshop on Delay-tolerant networking, pp. 252-259. ACM, 2005. Han, Bo, Pan Hui, VS Anil Kumar, Madhav V. Marathe, Jianhua Shao, and Aravind Srinivasan. "Mobile data offloading through opportunistic communications and social participation." IEEE Transactions on Mobile Computing, vol 11, no. 5 (2012): 821-834. Cuervo, Eduardo, Aruna Balasubramanian, Dae-ki Cho, Alec Wolman, Stefan Saroiu, Ranveer Chandra, and Paramvir Bahl. "MAUI: making smartphones last longer with code offload." In Proceedings of the 8th international conference on Mobile systems, applications, and services, pp. 49-62. ACM, 2010. Kosta, Sokol, Andrius Aucinas, Pan Hui, Richard Mortier, and Xinwen Zhang. "Thinkair: Dynamic resource allocation and parallel execution in the cloud for mobile code offloading." In Proceedings of IEEE INFOCOM2012 , pp. 945-953. IEEE, 2012.

[16]

[17]

[18]

[19]

[20]

[21]

Pietiläinen, Anna-Kaisa, Earl Oliver, Jason LeBrun, George Varghese, and Christophe Diot. "MobiClique: middleware for mobile social networking." In Proceedings of the 2nd ACM workshop on Online social networks, pp. 49-54. ACM, 2009. Jung, Sewook, Uichin Lee, Alexander Chang, Dae-Ki Cho, and Mario Gerla. "Bluetorrent: Cooperative content sharing for bluetooth users." Pervasive and Mobile Computing vol. 3, no. 6 (2007): 609-634. Shi, Cong, Vasileios Lakafosis, Mostafa H. Ammar, and Ellen W. Zegura. "Serendipity: enabling remote computing among intermittently connected mobile devices." In Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing, pp. 145-154. ACM, 2012. Li, Yujin, and Wenye Wang. "Can Mobile Cloudlets Support Mobile Applications?" In Proc. of IEEE INFOCOM2014. 2014. Shi, Cong, Mostafa H. Ammar, Ellen W. Zegura, and Mayur Naik. "Computing in cirrus clouds: the challenge of intermittent connectivity." In Proceedings of the first edition of the MCC workshop on Mobile cloud computing, pp. 23-28. ACM, 2012. Liu, Shu, and Aaron D. Striegel. "Exploring the potential in practice for opportunistic networks amongst smart mobile devices." In Proceedings of the 19th annual international conference on Mobile computing & networking, pp. 315-326. ACM, 2013. Huang, Di, Sanfeng Zhang, and Zhou Chen. "An Optimal Stopping Decision method for Routing in opportunistic networks." In Wireless Communications and Networking Conference (WCNC), 2013 IEEE, pp. 2074-2079. IEEE, 2013. Hui, Pan, Jon Crowcroft, and Eiko Yoneki. "Bubble rap: Social-based forwarding in delay-tolerant networks." IEEE Transactions on Mobile Computing vol. 10, no. 11 (2011): 1576-1589. Lindgren, Anders, Avri Doria, and Olov Schelén. "Probabilistic routing in intermittently connected networks." ACM SIGMOBILE mobile computing and communications review vol. 7, no. 3 (2003): 19-20. Liu, Cong, and Jie Wu. "An optimal probabilistic forwarding protocolin delay tolerant networks." In Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing, pp. 105-114. ACM, 2009. Zhou, Tao, Linyuan Lü, and Yi-Cheng Zhang. "Predicting missing links via local information." The European Physical Journal B 71, no. 4 (2009): 623-630. Cai, Qing-Song, and Jian-Wei Niu. "Time Evolving Graph Model for Opportunistic Networks Based on Edge-independent Evolution." Computer Engineering vol.15 (2011): 007. Yang, Yue, and Huijie Yang. "Complex network-based time series analysis."Physica A: Statistical Mechanics and its Applications 387.5 (2008): 1381-1386. Hu, Yu-Peng, Hao Luo, Ya-Ping Lin, Zheng Qin, and Bo Yin. "Spatiotemporal periodic behavior mining algorithm for social networks." Journal on Communications 34 (2013): 1. Lü, Linyuan, and Tao Zhou. "Link prediction in complex networks: A survey."Physica A: Statistical Mechanics and its Applications 390, no. 6 (2011): 1150-1170. Liben ‐ Nowell, David, and Jon Kleinberg. "The link ‐ prediction problem for social networks." Journal of the American society for information science and technology 58, no. 7 (2007): 1019-1031. Guimerà, Roger, and Marta Sales-Pardo. "Missing and spurious interactions and the reconstruction of complex networks." Proceedings of the National Academy of Sciences 106, no. 52 (2009): 22073-22078.