Community-Aware Opportunistic Routing in Mobile Social Networks

Transcription

1 IEEE TRANSACTIONS ON COMPUTERS VOL:PP NO:99 YEAR 213 Community-Aware Opportunistic Routing in Mobie Socia Networks Mingjun Xiao, Member, IEEE Jie Wu, Feow, IEEE, and Liusheng Huang, Member, IEEE Abstract Mobie socia networks (MSNs) are a kind of deay toerant network that consists of ots of mobie nodes with socia characteristics. Recenty, many socia-aware agorithms have been proposed to address routing probems in MSNs. However, these agorithms tend to forward messages to the nodes with ocay optima socia characteristics, and thus cannot achieve the optima performance. In this paper, we propose a distributed optima Community-Aware Opportunistic Routing () agorithm. Our main contributions are that we propose a home-aware community mode, whereby we turn an MSN into a network that ony incudes community homes. We prove that, in the network of community homes, we sti can compute the minimum expected deivery deays of nodes through a reverse Dijkstra agorithm and achieve the optima opportunistic routing performance. Since the number of communities is far ess than the number of nodes in magnitude, the computationa cost and maintenance cost of contact information are greaty reduced. We demonstrate how our agorithm significanty outperforms the previous ones through extensive simuations, based on a rea MSN trace and a synthetic MSN trace. Index Terms Community, Deay Toerant Networks, Mobie Socia Networks, Opportunistic Routing. 1 INTRODUCTION Mobie socia networks (MSNs) are a specia kind of deay toerant network (DTN), in which mobie users move around and communicate with each other via their carried short-distance wireess communication devices. Typica MSNs incude pocket switch networks, mobie vehicuar networks, mobie sensor networks, etc [1]. As more users expoit portabe short-distance wireess communication devices (such as smart phones, ipads, mobie PCs, and sensors in vehices) to contact and share data between each other in a cheap way, MSNs attract more attention. Since MSNs experience intermittent connectivity incurred by the mobiity of users, routing is a mainy concerning and chaenging probem. Recenty, some socia-aware routing agorithms that are based on socia network anaysis have been proposed, such as Bubbe Rap [2], [3], and agorithms in [4 7], etc. Two key concepts in socia network anaysis are: (i) community, which is a group of peope with socia reations; (ii) centraity, which indicates the socia reations between a node and other nodes in a community. Based on the two concepts, these agorithms detect the communities and compute the centraity vaue for each node. Messages are deivered via the nodes with good centraities. Since socia reations of mobie users generay have ong- M. Xiao and L. Huang are with the Schoo of Computer Science and Technoogy, University of Science and Technoogy of China, Hefei, 2327, China. E-mai: xiaomj, shuang@ustc.edu.cn J. Wu is with the Department of Computer and Information Sciences, Tempe University, 185 N. Broad Street, Phiadephia, PA E-mai: jiewu@tempe.edu Fig. 1. An exampe of mobie socia network. term characteristics and are ess voatie than node mobiity, socia-aware agorithms outperform traditiona DTN agorithms, such as fooding-based agorithms [8, 9] and probabiity-based agorithms [1 14]. Despite this, these agorithms tend to forward messages to the nodes with ocay best centraities. In this paper, we focus on the singe-copy routing probem in MSNs. In many rea MSNs, mobie users that have a common interest generay wi visit some (rea or virtua) ocation that is reated to this interest. For instance in Fig. 1, students with a common study interest wi visit the same cassrooms to take part in the same courses; customers with the same shopping interests often visit the same shops; friends generay share some resources through facebook, and so on. Based on this basic socia characteristic, we propose a home-aware community mode. Mobie users with the common interest autonomousy form a community, in which the frequenty visited ocation is their common home. Moreover, ike [1], we assume that each home supports a rea or virtua throwbox [15], a oca device that can temporariy store and transmit messages. Under the home-aware community mode, we pro-

2 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., pose a distributed optima Community-Aware Opportunistic Routing agorithm (). We first turn the routing between ots of nodes to the routing between a few community homes. Then, we adopt the optima opportunistic routing scheme by maintaining an optima reay set for each home. Each home ony forwards its message to the node in its optima reay set and ignores other reays. Since this scheme soves the probem of whether a home shoud seect a visited node as the reay of message deivery or ignore this visited node to wait for those better reays, it can achieve the optima performance. More specificay, our major contributions are summarized as foows: 1) We present a home-aware community mode and extend the centraity concept from a singe node to a group of nodes. Unike existing community modes, each community home in our mode is assumed to have a throwbox to store and transmit messages. 2) We present a rue of optima opportunistic routing through a theoretica anaysis. We design a reverse Dijkstra agorithm to determine the optima reays and compute the minimum expected deivery deay. Based on this, the agorithm can achieve the optima opportunistic routing performance. 3) We turn the routing in V mobie nodes into a routing in L ( L V ) community homes by virtue of the home-aware community mode. Moreover, we prove that the simpification wi not sacrifice the routing performance. As a resut, the network scae and the maintaining costs are reduced significanty. 4) We first design the agorithm for the case that each home has a rea throwbox. Then, we extend it to the case of virtua throwbox by etting the members of a community with high centraities to act as the home of this community. Simuation resuts show that it can achieve a neary optima performance. The rest of the paper is organized as foows. We introduce the network mode in Section 2. Section 3 is the socia network mode. The overview, detaied impementation, and extension of are presented in Sections 4, 5, and 6, respectivey. In Section 7, we evauate the performance of our agorithms through extensive simuations. After reviewing reated work in Section 8, we concude the paper in Section 9. A proofs are presented in the Appendix. 2 NETWORK MODEL & ASSUMPTIONS We consider an MSN composed of V nodes V = {v v V } moving among L ocations L={ L} ( L V ). Each mobie node visits a few ocations frequenty, whie visiting the others rarey. A typica MSN is the Wi-Fi campus network at Dartmouth Coege [16]. In this network, over 6, different users v,, d, S λ v,, λ S, R i S i,j D i,d (S) B, (S) TABLE 1 Description of auxiiary variabes. v is a node, is a ocation or home, d is a destination, and S is a set of nodes or homes. the exponentia distribution parameter of that node v and (any node in) node set S visit home. the optima reay set for the opportunistic routing from a message sender (i) to destination d. the optima betweenness set for the message deivery from home i to j. When the context is cear, the subscripts are removed. the minimum expected deivery deay from i to d via reay set S, where i may be a node, or a home. Specificay, D i,d =D i,d ( R i ) when S = R i. the betweenness of S, i.e., the expected deivery deay from home to ony via node set S. (i.e., students and facuty equipped with devices such as PDAs, aptops, and phones) move among about 5 recorded access points (APs) instaed in over 19 buidings, incuding the coege s academic buidings, the ibrary, and the student residences, etc. Moreover, previous works observed that 5% of mobie users in this network spent 74.% of their time at a singe AP to show the characteristic of frequenty visiting a few ocations [17]. Another MSN that foows this characteristic is the mobie vehicuar network, in which ots of buses and taxies move among bus stations and taxi stops. In this paper, we ca the frequenty visited ocations homes. Like in the previous work, we assume that the behavior of each mobie node visiting homes foows the Poisson process. In other words, the time interva that each node visits a home foows an exponentia distribution (the unit of time is time sot). This is consistent with most rea traces. Many previous works, such as [5, 14], aso make a simiar assumption. Moreover, if a node stays at a home for a ong time during each visit, it wi be approximatey treated as that the node visits the home mutipe times, and stays for a unit time during each visit. Besides, message transmissions happen ony when nodes visit homes. Here, we assume that the occasiona meeting outside of the homes cannot provide the message transmission, due to imited meeting time. We aso assume that each home has a throwbox [15], which has the abiity to store and transmit messages. In fact, many MSNs foow this assumption. For instance, the Road Side Units (RSUs) in mobie vehicuar networks are a kind of rea throwboxes. The APs in the Wi-Fi campus network can aso be seen as a type of rea throwboxes since each user can upoad/downoad data from network storages via these APs. For other MSNs without rea throwboxes, we et the nodes that frequenty visit or reside in a home act as the virtua throwboxes of this home. In the foowing, we first consider the case of rea throwbox. And then, we extend our soution to the case of virtua throwbox in Section 6. In addition,

3 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., home node Fig. 2. Exampe: home-aware communities. we assume that there are no stabe wired inks between these throwboxes, especiay for those virtua throwboxes. In fact, if there is a wired ink between two throwboxes and the cost of message deivery between them is negigibe, we can combine them as one throwbox. Based on the above descriptions, we assume that each node v V ony visits a few homes most of the time, and the interva of v s visit home L foows the exponentia distribution with the parameter λ v,. Then, our objective is to design a singe-copy routing agorithm with the minimum expected deivery deay. For ease of presentation, we ist the main auxiiary variabes in Tabe 1. 3 SOCIAL NETWORK MODELING Before presenting our agorithm, we buid the community and define two socia metrics in this section. 3.1 Buiding Home-Aware Communities In this paper, we propose a concept of home-aware community. A home-aware community is a community of nodes that frequenty visit a given home. The frequenty visited home is the common home of the community members, i.e., the community home. Moreover, if a node visits severa homes frequenty, it can beong to mutipe communities and have mutipe homes. Concretey, we define the community as foows: Definition 1: Home-Aware Community: a home-aware community C is a set of nodes that frequenty visit home (beyond a given threshod). That is: C ={v λ v, ε, v V }. (1) Moreover, home is equipped with a rea or virtua throwbox, so that it can be used as a reay of message deivery. Based on the definition, each community has a star topoogy where its home is the center. The whoe network is composed of some overapped star-topoogy communities, as shown in Fig.2. A community can easiy be detected. Each node v ony needs to estimate the parameter λ v, for each home, based on the history records. Then, it can find the communities that it beongs to according to Definition 1. Moreover, if a node beongs to a community, it means that the node frequenty visits the community home due to some interest. Each community exacty contains a group of nodes that have the common interest to the community home. 3.2 Centraity Metric In an MSN, the centraity metric is generay used to measure the importance of nodes during message deivery. A node with a better centraity vaue means that it has a stronger capabiity of connecting with other nodes. Previous works mainy adopt three centraity measures: degree centraity, coseness centraity, and betweenness centraity [3]. Degree centraity is measured as the number of direct inks between a given node and other nodes. Coseness centraity is a measure of how ong it wi take to deiver a message from a given node to other nodes. Betweenness centraity measures the extent to which a node ies on the paths inking other nodes. In this paper, we mode the whoe network into some overapped star-topoogy communities. The message deivery thus can be turned into the deivery within and/or between these communities. Accordingy, we ony present an intra-community centraity metric and an inter-community betweenness metric for nodes, to measure their importance in the message deivery within and between these communities, respectivey. A. Intra-Community Centraity In intra-community routing, the most concern is measuring the capabiity of each community member to meet and deiver messages to other members. Since intra-community message deiveries happen ony when nodes visit community homes, the smaer the expected deay to visit a community home, the higher capabiity to deiver messages a community member woud have. In fact, the expected deay for a node v to visit a community home, denoted by D v,, can be simpy derived from the parameter λ v,. That is, D v, = 1/λ v,. Therefore, we can directy use this vaue to measure the intra-community centraity of the node to the community. Definition 2: Intra-Community Centraity : I (v) is the reciproca of the expected deay for node v visiting a community home, i.e., I (v) =1/D v, =λ v,. According to Definition 2, the node with the argest intra-community centraity in a community has the best capabiity to deiver messages. In our extension (Section 6), we wi use such nodes to act as virtua throwboxes in the communities. B. Inter-Community Betweenness In this paper, we adopt the opportunistic routing scheme, in which mutipe nodes cooperativey deiver messages. It can be defined as foows. Definition 3: Opportunistic Routing: each message sender (home or node) has a reay set (homes or nodes). Once a reay in the set meets the message sender, the sender wi et this reay deiver messages. In other words, the first reay in the set to meet the message sender wi act as the rea reay.

4 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., To the first visit node ' In Section 5, we present an agorithm (Agorithm 1) to determine the optima betweenness set for each pair of overapped communities. These optima betweenness sets wi be used to deiver messages by. S Fig. 3. Opportunistic routing between communities (opportunistic routing via a set of nodes can be seen as a message deivery via a virtua node). This dynamica routing scheme is more genera than the routing based on a singe fixed reay. Based on this scheme, we extend the concept of betweenness from a singe node to a node set. Concretey, we define the inter-community betweenness to measure the abiity of a node set to be taken as a communication bridge between communities. Moreover, we use the deivery deay to evauate the inter-community betweenness of a set of nodes. Definition 4: Inter-Community Betweenness: B, (S) is the expected deivery deay that it takes for a reay set S (S C C ) to cooperativey deiver messages from community home to. The smaer the B, (S), the better the deivery abiity of S wi be. According to the opportunistic routing scheme, a node in the reay set acts as the rea reay ony when it is the first node in the set to meet the message sender, as shown in Fig. 3. Thus, we can compute the intercommunity betweenness of a given node set by the foowing theorem. Theorem 1: For two overapped communities C, C and an arbitrary reay set S (S C C ), we have: B, (S)= 1 v S λ v, + ' v S λ v,/λ v, v S λ. (2) v, Proof: See Appendix A. In Eq.(2), the first part B (1) 1, = v S λ actuay v, indicates the expected deay that the first node in S visits, and the second part B (2), = v S λ v,/λ v, v S λ is v, the average deay of the nodes when S forwards a message to. For simpicity, we can see the whoe set as one entity, and treat it just as a virtua node S, whose λ parameter is λ S, = v S λ v, and the average deivery deay to is B (2),, as shown in Fig.3. Note that the betweenness vaues of the virtua node is the same as that of the origina reay set, i.e., B, (S)= 1 λ S, +B (2),. For an arbitrary pair of overapped communities C and C, there are 2 C C different reay sets. There must be a reay set that has the smaest betweenness. We define this set as the optima betweenness set. Definition 5: Optima Betweenness Set: S, is the reay set with the smaest betweenness for the message deivery from community home to. Concretey, S, = argmin B, (S). (3) S C C 4 OVERVIEW OF In this section, we introduce the methodoogy and basic idea of. Here, we assume that the source (and reays) knows which communities that the destination d beongs to. That is, the message consists of the source, the destination information, and the data to be deivered. This assumption is reasonabe because the source generay knows some basic information about the destination in most message deivery tasks. In fact, the source has many ways to know the basic information of the destination. For exampe, the destination can broadcast this information to a community homes, or a naming service is used to distribute this information, etc. A simiar assumption is aso adopted in previous work [5]. 4.1 Methodoogy: Optima Opportunistic Routing The optima opportunistic routing scheme means that each message sender deivers messages via its optima reay set (i.e., deivers messages via the first encountered reay in this set). The key probem is to determine whether a reay beongs to the optima reay set for each message sender. To this end, we derive an optima opportunistic routing rue. Without oss of generaity, we consider an opportunistic routing from a message sender i to the destination d via some candidate reays {u λ i,u > }. Here, the message sender i might be a mobie node or a home. Each u is a one-hop reay of i, i.e., λ i,u >, but it does not must be a one-hop reay of the destination. The optima reay set, denoted by R i, is given by the foowing formua: R i = argmin D i,d (S). (4) S {u λ i,u >} In Eq.(4), D i,d (S) is the expected deay for i deivering messages to d via the reay set S. Moreover, for simpicity, we et D i,d =D i,d ( R i ). (5) Then, the optima opportunistic routing rue is presented as foows. Theorem 2: Optima Opportunistic Routing Rue: the message sender aways deivers messages to the encountered reay that has a smaer minimum expected deay to the destination than itsef. Concretey, a reay u beongs to the optima reay set R i for the deivery from i to d, if and ony if, D u,d <D i,d, i.e.: u R i D u,d <D i,d (6) Proof: See Appendix B.

5 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., S,' ' (a) Buid a virtua ink, ', D', ' ' 1 D',, ', D', ' ' k { k+1,, n } {, 1,, k } ' ' Fig. 5. Iterativey compute the minimum expected deivery deay. (b) Simpify the whoe network Fig. 4. An exampe of network simpification. According to Theorem 2, we ony need to compute and compare the minimum expected deivery deays from the message sender and the reay to the destination. Then, we can determine whether the reay beongs to the optima reay set of the sender. 4.2 The Basic Idea The agorithm consists of two phases: the initiaization phase and the routing phase. The initiaization phase simpifies the network with V nodes to the network with L community homes through the socia network modeing. Then, under the simpified network, the routing phase deivers messages based on the optima opportunistic routing rue. Based on the socia network modeing and the optima opportunistic routing rue, can achieve the optima performance with a sma cost. More specificay, the basic idea of is presented as foows. A. The Initiaization Phase In the initiaization phase, each community home coects the optima betweenness set of each pair of community homes and uses these information to ocay construct a contact graph of these homes. First, each community home determines the optima betweenness sets for the message deiveries from itsef to other community homes. Given the parameters λ v, and λ v, for each node v in community C and another overapped community C, i.e., {λ v,, λ v, v C C }, the optima betweenness set S, can be determined through a greedy agorithm (Agorithm 1 in Section 5). Ony the nodes in optima betweenness sets wi be used to deiver messages. Second, home treats the whoe optima betweenness set S, as a virtua node, and buids a virtua ink for the message deivery from to via S,. Moreover, this ink is attached with a weight λ,, D,, as shown in Fig. 4(a). The time interva that the virtua ink emerges foows the exponentia distribution with the parameter λ,. The expected deivery deay via the virtua ink is D, (i.e., the deay for the optima betweenness set to forward the messages to home ). Moreover, the weight satisfy: λ, = λ, S, = D, = B(2), = v S, λ,v ; (7) v S λ,,vd v, v S λ. (8),,v Finay, home sends the ink weight λ,, D, to, and receives ink weights from, other homes. Based on these ink weights, home constructs a direct weighted graph G = L, W, where W = { λ,, D,, L}, as shown in Fig. 4(b). In addition, when the ink weight λ,, D, changes by more than a threshod aong with the time ecipse, home aso wi send the updated weight to other homes. B. The Routing Phase The routing phase computes the minimum expected deivery deays and makes the routing decision based on the optima opportunistic routing rue when a node v visits a community home i. First, node v gets the direct weighted graph G from home i, and extends this graph to G + = L +, W + by adding the destination and itsef. For simpicity, we treat v and d as two virtua homes, i.e., n = v (n = L +1) and = d. Moreover, we et L + = L + { n, }, and W + =W + { λ n,,, λ,n,, λ,l, L}. Second, in the extended graph G +, home n (i.e., node v) computes the minimum expected deivery deays D n, and D i, through a reverse Dijkstra agorithm (Agorithm 3 in Section 5). The basic idea is to compute the minimum expected deivery deays from homes or nodes in L + to the destination in an ascending order. Without oss of generaity, we assume that L + = {, 1,, n }, and the minimum expected deivery deays for each home in set S ={, 1,, k } (i.e., D,,, D k, ) have been cacuated, as shown in Fig. 5. Then, we compute the expected deay from each home L + S = { k+1,, n } to home via S, according to the foowing formua λ, e S λ, t is the probabiity density for the message deivery via ; D, +D, is the expected deay for the optima betweenness set of and to forward the message to pus the expected deay from to.

6 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., D, = S λ, e S λ, t (t+d, +D, )dt = 1+ S λ, (D, +D, ) S λ,. (9) Assume that D, is the smaest when = k+1. Then, this deay is exacty the minimum expected deivery deay of k+1. In the same way, D k+2,,, D n, can be iterativey derived. Finay, home n (i.e., node v) compares D n, and D i, and ets the one with a smaer deay vaue receive the message. 4.3 Optimaity of First, we show that can achieve the minimum expected deivery deay in the simpified network. As the description in Section 4.2, uses a reverse Dijkstra agorithm to cacuate the minimum expected deivery deay from each home to the destination in the extended graph G +. The minimum expected deivery deays wi be derived in an ascending order. When we compute the (k+1)-th minimum expected deivery deay, the deays smaer than this one have been derived out. According to the optima opportunistic routing rue in Theorem 2, ony these homes can be candidate reays of the home with the (k + 1)-th minimum expected deivery deay. Thus, Eq.(9) can correcty derive the minimum expected deivery deays of a homes to the destination. Second, we can get that the minimum expected deivery deays that are derived in the simpified network are equa to the corresponding vaues in the origina network. In fact, this is ensured by the foowing theorem. Theorem 3: Assume that community C has m overapped communities C 1,, C m. Then, the optima reay set R of home, and the optima betweenness sets S,i (1 i m) satisfy: 1) if v m i=1 S,i, then v R ; 2) S,i R, otherwise S,i R = for i [1,m]. Proof: See Appendix C. Theorem 3 shows that either a nodes in the optima betweenness set S,i, or none of them, beong to the optima reay set R ; furthermore, if a node does not beong to any optima betweenness set, it aso does not beong to the optima reay set. This means that the simpified network sti contains a the nodes that beong to the optima reay sets, and that the each optima betweenness set can act as a reay as a whoe. Thus, the minimum expected deivery deays that are derived in the simpified network are equa to the resuts in the origina network. Based on the above anaysis and the optima opportunistic routing rue in Theorem 2, we can straightforwardy get the optimaity of. That is, v 1,=1/1 v 1 v 2,=1/ 1 v 2 v 3,=1/2 v 3 v 1, =1/ ' 2 v 2',=1/3 ' v 3, =1/8 (a) A simpe MSN ' B, ' {v 1 } {v 1,v 2 } ~ S, ' (b) Betweenness vs. set {v 1,v 2,v 3 } Fig. 6. Exampe: determine optima betweenness set. Coroary 1: can achieve the minimum expected deivery deay. 4.4 Discussion: Overhead of makes the routing decision on a simpified network. The simpification process has two advantages. On the one hand, the network with O( V 2 ) edges is turned into a network with O( L 2 ) edges. The computation, storage and communication costs are significanty reduced, since L V (e.g., the V 2 / L 2 of the rea MSN trace used by our evauation in Section 7 is about 1,). On the other hand, the edge weights of a simpified network ony depend on the optima betweenness sets. The behavior of the nodes outside optima betweenness sets woud not resut in the update of edge weights. In genera, each optima betweenness set ony incudes severa nodes that frequenty visit the community homes. The occasiona visit behavior woud not resut in an update of the edge weights. In fact, these frequent visit behaviors indicate the potentia socia reationships between communities, which show ong-term characteristics. For exampe, the dependency between an educationa course community and a research community in a campus socia network is a ong-term socia characteristic; students in a research community woud periodicay take part in corresponding fundamenta courses; this even woud not be vioated by the enroment of new students and the graduation of od students. The reationship between departments in a company or institution is aso a ong-term socia characteristic, which woud not be vioated by empoyment variation, and so on. Thus, the updating and management costs of the shared network information are aso significanty reduced. These two advantages make abe to achieve the optima performance with a sma cost, which is very important to rea MSNs. 5 DETAILED IMPLEMENTATION OF This section introduces the detaied impementation of, incuding the initiaization phase and the routing phase. The first phase simpifies the network (Agorithm 2), and the second phase computes the minimum expected deivery deay (Agorithm 3) and makes the routing decision (Agorithm 4). Both of the phases are impemented in the distributed way.

7 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., Agorithm 1 Determine optima betweenness set Require: { λ v1,, λ v1,,, λ v n,, λ vn, } (λ v1, λ v n, ) Ensure: S,, λ,, D, 1: Initiaize: S ={v 1 } and D, (S)= 1 λ + 1 v1, λ ; v1, 2: for i=2,, n do 3: S =S+{v i }; 4: Incrementay compute D, (S) by Eq.(2); 5: if D, (S) increases then 6: Break; 7: return S, =S {v i } and corresponding λ,, D, ; 5.1 Initiaization Phase The key of the initiaization phase is to determine the optima betweenness sets for each pair of communities. To this end, we introduce a theorem, by which these optima betweenness sets can be efficienty derived out. In previous work [14], Conan et a. expoit the fixed point technique to design an efficient agorithm, which can be used to determine the optima betweenness set S. In fact, the resuts, incuding a property and the corresponding agorithm, aso can be derived from our optima opportunistic routing rue in Theorem 2. For the integrity of this paper, we introduce them here, as shown in Coroary 2 and Agorithm 1. Coroary 2: Assume that λ v1, λ v 2, λ v, n, then the optima betweenness set S, satisfies: 1) v 1 S, ; 2) if v i+1 S,, then v i S,. That is, k [1, n] s.t. S, ={v 1,, v k }; 3) if S, = {v 1,, v k }, then B, ({v 1,, v i }) > B, ({v 1,, v i, v i+1 }) for any i [1, k 1]. Proof: See Appendix D. The agorithm to determine S,, based on Coroary 2, is greedy. The basic idea [14] is to add nodes v 1, v 2,, v n into S, in turn, to extend the reay set unti the corresponding deivery deay B, ( S, ) increases; then, end the extending operation and get S,. Concretey, S, is initiaized in step 1, and is extended in step 3. Step 4 computes the minimum expected deay according to Eq.(2). The correctness of this agorithm is provided by Coroary 2. The first property of the theorem ensures the correctness of the initiaization of S,, the second property ensures the correctness of the extended S,, and the third property ensures the correctness of ending the extending operation. The computationa overhead of this agorithm is O( C C ). Fig. 6 shows an exampe of greediy determining the optima betweenness set. There are three reays v 1, v 2, v 3 for message deivery from to, as shown in Fig. 6(a). The optima betweenness set S is determined by adding nodes v 1, v 2, v 3 into S, in turn, and Agorithm 2 : initiaization Ensure: G= L, W, where W ={ λ,, D,, L} For each community home L do 1: Coect λ v,, λ v, for each v C and L {}; 2: Use Agorithm 1 to produce S, and λ,, D, ; 3: Create the virtua ink : λ,, D, for each L {} and send the ink weights to other homes; 4: Receive the ink weights from other homes; 5: Construct the contact graph G= L, W ; finding the minimum D, ( S, ). When S, ={v 1 }, the expected deay is 12. When node v 2 is added into S,, the expected deay decreases to be 15/2. However, after node v 3 is added into S,, the expected deay increases to become 55/7, as shown in Fig. 6(b). Then, the optima reay set S, = {v 1, v 2 }. Note that the optima reay for singe path routing might not be the optima reay for opportunistic routing. In this exampe, though node v 3 is the best reay for the singe path deivery from to, it does not beong to S,. Now, we present the impementation of the initiaization phase by Agorithm 2. Each community home first coects the λ parameters of its community members in Step 1. Then, the home expoits Agorithm 1 to determine the optima betweenness sets for the message deiveries from itsef to other community homes in Step 2. In Step 3, the home produces the virtua inks for these deiveries and sends the corresponding weights to other community homes. Next, the home receives the ink weights of other pairwise community homes to ocay construct the contact graph of homes in Steps 4 and 5. Note that the agorithm is a distributed one. The correctness is provided by Coroary 2. The computationa overhead is dominated by the cost of determining the optima betweenness sets in Step Routing Phase The routing phase extends the graph, uses the reverse Dijkstra agorithm to compute the minimum expected deays for each home in the extended graph, and then makes the routing decision. The reverse Dijkstra agorithm is shown in Agorithm 3. Steps 1 and 2 are the initiaization. In each round, i.e., Steps 4-9, the minimum expected deivery deay of a home is determined. An exampe is shown in Fig. 7. The correctness is provided by Eq.(9) and the optima opportunistic routing rue. The computationa overhead is O( L 2 ). The routing decision of is shown in Agorithm 4. When a node v visits a community home, it first construct the extended contact graph of homes G + in Step 4 by adding v and d into the graph G, which is generated by home in the initiaization phase. Then, node v uses Agorithm 3 to compute

8 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., /4,1 1/2,2 1/2,5 1/4,1 1/2,2 2 ' 1 2 D 1,' =4 ' 1 2 D 1,' =4 D 2,' =4 ' 1 2 D 1,' =4 D 2,' =4 ' 1 2 D 1,' =4 D 2,' =4 ' 1/2,5 1/1,5 1/2, D 3,' =25 D,' =25 3 D 3,' =25 (a) simpified netwrok (b) comp. D 1, (c) comp. D 2, (d) comp. D 3, (e) comp. D, Fig. 7. An exampe of iterativey computing minimum expected deays: in each round, the minimum expected deay of a home is determined according to Eq.(9)( S 1, = S 2, = S 3, ={ }, S, ={ 1, 2 }). Agorithm 3 Compute minimum expected deay Require: G + = L +, W +, i, =d Ensure: D i,d 1: Set S = ; 2: Let D, =, S, and L + =L + ; 3: for each L + do 4: Compute D, (S) according to Eq.(9); 5: Seect the smaest one, and et D, =D, (S); 6: if is i then 7: Break; 8: ese 9: S, and L + =L + ; 1: return D i,d =D, ; the minimum expected deivery deays D v,d and D,d in Step 5. The routing decision is made in Steps 6-9. The computationa overhead of this agorithm is dominated by the execution of Agorithm 3 in Step 5. Moreover, the rue of optima opportunistic routing ensures that this agorithm can achieve the minimum expected deay for each message deivery. 6 EXTENSION In this section, we extend the agorithm to the case that community homes have no abiity to store messages. Generay, there are many nodes that reside in these homes of very high probabiities, according to the rea traces of MSNs. We thus can use these nodes to act as the message reays, i.e., virtua throwboxes, for this case. For simpicity, we assume that the average residua time of each node for each visit is τ. Here, the residua time τ aso means that if the time interva of two nodes that are visiting the same home is no more than τ, then they can exchange messages. Under this mode, we can compute the residua probabiity of a node v visiting a home, denoted by r v,, by the foowing formua: r v, = 1 t e λv,t (λ v, t) k kτ k! k=1 = λ v, τ. (1) In this formua, e λ v, t (λ v, t) k k! is the probabiity that v visits for k times. Note that λ v, is actuay the visit Agorithm 4 : routing For each node v V do 1: if v visits a community home L then 2: for each message of v and, v do 3: Extract destination (d) information; 4: Get G + by adding v and d to G in home ; 5: Compute D v,d and D,d through Agorithm 3; 6: if D v,d <D,d then 7: Let v hod the message; 8: ese 9: Let hod the message; frequency of node v to the community home in a unit time, and τ is the stay time of each visit. Thus, we aways have r v, = λ v, τ 1. Moreover, the direct deivery deay of two community members, v and v, satisfy the foowing formua: D v,v = = t r v,λ v, e r v, λ v,t dt 1 1 = λ v, r v, λ v, λ v,τ (11) Here, it shoud be stated that even though the average residua time is assumed to be the same for the sake of simpicity, the formuas are sti correct if they are different. Compared to the case where the community homes have storage abiities, the probabiity parameter for node v visiting the home becomes λ v, r v, from λ v,. It is mutipied by a coefficient r v, that is near to 1. Thus, after repacing the λ v, in the agorithm by λ v, r v,, the agorithm can sti achieve a neary optima performance. 7 PERFORMANCE EVALUATION In this section, we conduct extensive simuations to evauate the performance of the agorithm using the MSN trace from the Wi-Fi campus network of Dartmouth Coege [16]. Since the other widey used MSN traces, such as the Infocom trace and the UMassDieseNet trace, have not provided the ocation information, we aso extend the evauation to a synthetic trace based on a Time-variant Community Mode [18]. We compare the agorithm with the existing socia-aware agorithms: [3] and

9 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., [2]. Three performance metrics commony used are examined: deivery ratio, deivery deay and deivery hops. Simuation resuts demonstrate that the agorithm can significanty improve MSN routing performance. 7.1 Agorithms in Comparison [3] is an MSN routing agorithm that is based on sma word dynamics. In this agorithm, a nove metric, Utiity, composed with betweenness and simiarity, is proposed; the ego network anaysis technique is used to estimate the vaues of the betweenness centraity metric and the simiarity metric for each node, based on oca information. When some nodes encounter each other, the agorithm ets the node with the maximum utiity vaue deiver messages. [2] is an MSN routing agorithm based on k-cique community detection. This agorithm uses the weighted network anaysis technique to detect the k-cique community, and computes centraity ranks for each node. Messages are forwarded (bubbe) up aong the hierarchica tree using the goba rank, and then bubbe up by using the oca rank when they reach nodes that are in the same community as the destinations. (r =.9) is the extended version of, where r =.9 means that each community has a node with a residua probabiity of.9. Here, we ony et r =.9 for simpicity. In fact, we get simiar simuation resuts for other residua probabiities. 7.2 Simuations on the Rea Trace We adopt the rea experimenta trace of the Wi-Fi campus network in Dartmouth Coege [16] in our simuations, since it is one of the most extensive and widey expoited data traces. This trace incudes 57 vaid APs and uses 6,22 og fies to ist the records for each node s visit to the APs from Due to the imit of our PC memory and computation abiity, we randomy seect partia mobie nodes and APs from the trace to construct an MSN, whie ensuring adequate connectivity of the network. Concretey, the network is buit as foows. (1) We first derive the number of reated nodes for each AP from the trace, and randomy seect an AP with enough reated nodes as the seed AP, denoted by 1. Here, a node is said to be reated to an AP if there are records about its visit to this AP in the trace. In addition, we use C i to denote the set of reated nodes of AP i. (2) Secondy, we assume that 1,, i 1 have been determined, and then we determine the i-th AP. We randomy seect an AP from the remaining APs, and compute C i C k for each k [1, i 1]. If there exists a k [1, i 1] to make C i C k > 8% C k, we consider this AP be very cose to k, and then we drop it and reseect a new AP. If C i C k <1% C k for a k [1, i 1], we consider this AP to not have enough connectivity to other APs, and thus we drop it and seect a new AP. We repeatedy seect APs and test the conditions unti a suitabe AP is found, and then et it be i. If an AP that satisfies the conditions cannot be found, then we return and restart from step (1). (3) We repeat step (2) unti C 1 C i V. If C 1 C i > V, we randomy remove some nodes to make C 1 C i = V. Then, we get L={ 1,, i }, and V =C 1 C i. Finay, we compute the λ parameter for each node s visit to each AP, according to the trace. After buiding the MSN, we conduct the simuations by generating 1, messages for randomy seected source nodes, and by executing the abovementioned agorithms to forward these messages to their destinations, whie recording the deivery deay, deivery ratio, and deivery hops. Moreover, we give each message a time-to-ive (TTL) vaue. Messages woud be dropped if their TTLs are exhausted. For the fair of the comparison, we set the deays of faied message deiveries as the maximum deay vaue, i.e., TTL, though their deivery hops might be very sma. In simuations on evauating the deivery ratio, we set the number of nodes to V =4, 6, 8, 1,, 1,2, and 1,4, respectivey. The TTLs are set from 1 week to 1 weeks. Simuation resuts are shown in Fig.8(a-f). In simuations on evauating the average deivery deay and average deivery hops, the TTL is 2 weeks. The resuts are shown in Fig.8(g-h). These resuts show that significanty outperforms and. Compared with and, increases the deivery ratio by about 89.5% and 35.8%, and reduces the deivery deay by about 49.6% and 22.7%, respectivey. We aso ist the contrast between the number of communities and nodes in Fig.8(i). It shows that the number of communities is far ess than the number of nodes. Since the routing decision of mainy depends on the number of communities, the computationa cost and maintenance cost are very ow. Moreover, aong with the increasing of nodes, the number of communities increases. Due to the increasing network scae, the deivery ratios of these agorithms have a itte decreases, and the average deivery deay of has a itte increase. However, the increasing of communities has no effect on the average deivery deays of and. This is because many message deiveries in both of the agorithms converge at the homes with oca high centraity vaues. The average deivery hops of the two agorithms are about two-hops, which aso proves their property of oca convergency. In contrast, there is no oca convergency in. In addition, we aso compare the performance of the extended agorithm, i.e., (r =.9)

10 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., (a) Number of nodes: V = 4 (b) Number of nodes: V = 6 (c) Number of nodes: V = 8 (d) Number of nodes: V = 1, (e) Number of nodes: V = 1, 2 (f) Number of nodes: V = 1, (r=.9) Number of Hops (g) Comparison of average deay (h) Comparison of average hops (i) Communities vs. nodes Fig. 8. Performance comparisons of, (r =.9),, and on the rea trace. with and, as show in Fig.8(a-h). The resuts show that the performances of (r =.9) are very cose to. 7.3 Simuations on the Synthetic Trace The synthetic trace in our simuations is produced by a Time-variant Community Mode in [18]. In this mode, each node is randomy assigned to severa community homes on a pane. Time is equay divided into timesots. In each timesot, nodes perform random waypoint trips with a probabiity 1 p of roaming outside and a probabiity p of staying inside (or getting back to) their homes. By choosing different probabiities p for each node, a arge range of heterogeneous node behaviors can be reproduced. More specificay, we set 1 2 homes, and et each node be randomy reated to 1 5 homes. The probabiity p of each node visiting a home is set to be a random vaue in [.1,.2]. Note that this community mode is a discrete version of our network mode described in Section 2, in which the parameter λ is actuay equa to the visiting probabiity p. Thus, the produced trace is consistent with our network mode. We execute agorithms, (r =.9),, and on this synthetic trace, respectivey. In the simuations, 1, messages are generated by randomy seecting source and destination nodes. The average deivery deay, deivery ratio, and deivery hops are recorded. In simuations on evauating the deivery ratio, we set V =12, 16, and 2,, respectivey. The number of community homes is set to be L =1, 15, and 2. The TTLs are set from 1 to 1 timesots. Simuation resuts are shown in Fig.9. In simuations on evauating the average deivery deay and average deivery hops, we et V =1,, 1,2,, 2, nodes. The number of community homes and TTL are the same as the simuations on the deivery ratio. The resuts are shown in Fig.1. These resuts aso show that, compared with Sim- Bet and, has a significanty arge deivery ratio and a ow average deivery deay, and (r =.9) has a performance cose to. Moreover, the average deivery deay of is neary irreative to the number of nodes. This is consistent with our theoretica anaysis. In fact, our

11 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Time (timesot) Time (timesot) Time (timesot) (a) V = 12, L = 1 (b) V = 16, L = 1 (c) V = 2, L = 1 Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Time (timesot) Time (timesot) Time (timesot) (d) V = 12, L = 15 (e) V = 16, L = 15 (f) V = 2, L = 15 Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Successfu Deivery Ratio (r=.9) Time (timesot) Time (timesot) (g) V = 12, L = 2 (h) V = 16, L = 2 (i) V = 2, L = 2 Fig. 9. Comparisons of deivery ratios of, (r =.9),, and on the synthetic trace. theoretica anaysis shows that message deiveries mainy depend on the number of communities and the nodes in optima reay sets. Other nodes wi not participate in the message deiveries. As a resut, there is ony a very sma variation with the number of nodes when we fix the number of communities. 8 RELATED WORK So far, many traditiona DTN routing agorithms have been proposed. These agorithms incude fooding-based agorithms (e.g., [8, 9]) and probabiity-based agorithms (e.g., [1, 11, 13, 14, 19, 2]). Among these agorithms, the MH agorithm [14] adopts the optima opportunistic routing strategy, based on goba contact information. Compared with this agorithm, the agorithm adopts the homeaware community mode and turns the routing probem among mobie nodes into the routing probem among static communities, and therefore, achieves the optima routing performance ony based on community contact information. The maintenance cost of the contact information is far ess than the MH agorithm. This is important because it means that the mobiity behaviors of most nodes woud not affect the. Time (timesot) routing performance of the whoe network. Moreover, since the network is simpified to be a static network, many previous routing agorithms in static networks, such as wireess sensor networks, can be appied. Socia-aware agorithms assume that each node has some socia characteristics (such as community, centraity, and simiarity, etc.) and then expoits the knowedge to direct the routing decision, so as to improve the deivery ratio. The [3] agorithm expoits the ego network technique to ocay compute the approximate centraity and simiarity for each node. It then uses these characteristics to find bridge nodes for the message deivery. The [2] agorithm uses the k-cique agorithm to detect a community, ranks each node by cacuating their centraity vaues, and then expoits the rank vaues of nodes to direct the routing decision. Besides, the agorithm in [5], a muticasting MSN agorithm, aso uses the k-cique technique to detect the communities, and defines the cumuative contact probabiity of each node as its centraity, based on which, it finds the reay for message deivery. The Socia-Greedy [21] agorithm cacuates the socia coseness for each node based on its socia profie, and then greediy deivers the messages to the nodes that are sociay coser to their

12 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., Average Deay (timesot) (r=.9) Average Deay (timesot) (r=.9) Average Deay (timesot) (r=.9) Number of Hops (r=.9) (a) L = Number of Hops (r=.9) (b) L = (c) L = (d) L = 1 (e) L = 15 (f) L = 2 Fig. 1. Comparisons of deay and hops of, (r=.9),, and on the synthetic trace. destinations. Compared with the agorithm, these agorithms just expoit the socia characteristics of nodes to improve the probabiity of meeting the destination for each message. However, this is sti unpredictabe, and thus cannot achieve the optima resut. The agorithm is based on the home-aware community mode. There are two features: one is that nodes are assumed to frequenty meet at some homes and the cases that they occasionay encounter at other paces are ignored; another is that the interva for each node s visit to homes foows the exponentia distribution. In fact, most of the mobiity research [17, 18, 22 24] has captured the characteristics of skewed ocation visiting preferences and the periodic re-appearance of nodes at the same ocation from numerous rea trace anayses. Moreover, they aso point out that the inter-meeting time of nodes in the rea traces foows the power aw distribution. However, Cai et a. [25] has proven that when the area is bounded, the distribution is the exponentia distribution; otherwise, if there is no bound, the distribution becomes power aw. Therefore, for simpicity, the exponentia distribution is sti widey adopted, as seen in [5, 14]. Compared with these mobiity modes, our mode does not remove the homes. Instead, we utiize these homes to reay messages. In addition, a ot of research aso uses some auxiiary nodes to reay messages: research in [15] expoits throwboxes to reay messages, and research in [26] uses mobie message ferries to reay transfer messages, etc. Compared with our work, message ferries are mobie message reays, unike our static community homes. The throwbox is just ike our community home; however, their works mainy focus Number of Hops (r=.9) on the capacity and deivery deay of the Epidemic agorithm when adding throwboxes into the DTNs. To the best of our knowedge, this is the first work to use home-aware communities to find the optima opportunistic routing among mobie nodes. 9 CONCLUSION In this paper, we mode an MSN into some overapping home-aware communities, simpify the routing probem among many mobie nodes into the probem among some static communities, and propose the agorithm to achieve optima opportunistic routing. Through theoretica anaysis, we find out that optima opportunistic routing ony depends on a few nodes in the network. A change in behavior of most nodes woud not affect the routing performance. We can thus achieve the optima routing performance at a very ow maintenance cost. Compared with previous socia-aware agorithms, the optima and predictabe routing performance is the biggest advantage of the agorithm. REFERENCES [1] J. Wu, M. Xiao, and L. Huang, Homing spread: Community home-based muti-copy routing in mobie socia networks, in IEEE INFOCOM, 213. [2] P. Hui, J. Crowcroft, and E. Yoneki, Bubbe rap: socia-based forwarding in deay toerant networks, in ACM MobiHoc, 28. [3] E. Day and M. Haahr, Socia network anaysis for routing in disconnected deay-toerant manets, in ACM MobiHoc, 27.

13 IEEE TRANSACTIONS ON COMPUTERS, VOL., NO., 213 [4] [5] [6] [7] [8] [9] [1] [11] [12] [13] [14] [15] [16] [17] [18] [19] [2] J. Wu and Y. Wang, Socia feature-based mutiieee/acm Transactions on Networking, vo. 16, path routing in deay toerant networks, in IEEE no. 1, pp , 28. INFOCOM, 212. [21] K. Jahanbakhsh, G. C. Shoja, and V. King, SociaW. Gao, Q. Li, B. Zhao, and G. Cao, Muticasting greedy: A sociay-based greedy routing agoin deay toerant networks: A socia network rithm for deay toerant networks, in MobiOpp, perspective, in ACM MobiHoc, Q. Li, S. Zhu, and G. Cao, Routing in sociay [22] L. Jeremie, F. Timur, and C. Vania, Evauating sefish deay toerant networks, in IEEE INFOmobiity pattern space routing for dtns, in IEEE COM, 21. INFOCOM, 26. R. Lu, X. Lin, and X. S. Shen, Spring: A socia- [23] T. Spyropouos, K. Psounis, and C. S. Raghavenbased privacy-preserving packet forwarding prodra, Performance anaysis of mobiity-assisted toco for vehicuar deay toerant networks, in routing, in ACM MobiHoc, 26. IEEE INFOCOM, 21. [24] P. Hui, A. Chaintreau, J. Scott, R. Gass, A. Vahdate and D. Becker, Epidemic routing J. Crowcroft, and C. Diot, Pocket switched netfor partiay-connected ad hoc networks, Duke works and human mobiity in conference enuniversity, Tech. Rep. CS-2-6, June 2. vironments, in ACM SIGCOMM Workshop on T. Spyropouos, K. Psounis, and C. Raghavendra, Deay-Toerant Networking (WDTN), 25. Spray and wait: An efficient routing scheme [25] H. Cai and D. Y. Eun, Crossing over the for intermittenty connected mobie networks, bounded domain: From exponentia to powerin ACM SIGCOMM Workshop on Deay-Toerant aw inter-meeting time in manet, in ACM MobiNetworking (WDTN), 25. Com, 27. A. Lindgren, A. Doria, and O. Scheen, Proba- [26] M. M. B. Tariq, M. Ammar, and E. Zegura, biistic routing in intermittenty connected net Message ferry route design for sparse ad hoc works, Lecture Notes in Computer Science, vo. networks with mobie nodes, in ACM MobiHoc, 3126, no. 1, pp , J. Burgess, B. Gaagher, D. Jensen, and B. N. Mingjun Xiao is an associate professor at Levine, Maxprop: routing for vehice-based the Schoo of Computer Science and Techdisruption-toerant networks, in IEEE INFOnoogy in University of Science and Technoogy of China. He received his Ph.D. degree COM, 26. from University of Science and Technoogy S. Jain, K. Fa, and R. Patra, Routing in a deay of China in 24. He is currenty a visiting toerant network, in ACM SIGCOMM, 24. schoar at Tempe University, under the supervision of Dr. Jie Wu. He has served as a C. Liu and J. Wu, Routing in a cycic mobisreviewer for many journa papers. His main pace, in ACM MobiHoc, 28. research interests incude deay toerant netv. Conan, J. Leguay, and T. Friedman, Fixed works and wireess sensor networks. point opportunistic routing in deay toerant netjie Wu is chair and Laura H. Carne proworks, IEEE Journa on Seected Areas in Commufessor in the Department of Computer and nications, vo. 26, no. 5, pp , 28. Information Sciences at Tempe University. Prior to joining Tempe University, he was M. Ibrahim, P. Nain, and I. Carreras, Anaysis a program director at the Nationa Science of reay protocos for throwbox-equipped dtns, Foundation and a distinguished professor at in WiOPT, 29. Forida Atantic University. His research interests incude: wireess networks, mobie comd. Kotz, T. Henderson, I. Abyzov, and puting, routing protocos, faut-toerant comj. Yeo, CRAWDAD data set dartmouth / puting, and interconnection networks. He has campus (v ), Downoaded from pubished more than 55 papers in various journas and conference proceedings. He serves in the editoria boards of IEEE Transactions on Computers and Journa of Parae Sep. 29. and Distributed Computing. Dr. Wu was aso genera co-chair for T. Henderson, D. Kotz, and I. Abyzov, The IEEE MASS 26, IEEE IPDPS 28, and DCOSS 29 and is changing usage of a mature campus-wide wire- the program co-chair for IEEE INFOCOM 211. He has served as an IEEE Computer Society distinguished visitor. Currenty, he is the ess network, in ACM MobiCom, 24. chair of the IEEE Technica Committee on Distributed Processing W. Hsu, T. Spyropouos, K. Psounis, and (TCDP), an ACM distinguished speaker and a Feow of the IEEE. A. Hemy, Modeing time-variant user mobiity Dr. Wu is the recipient of 211 China Computer Federation (CCF) Overseas Outstanding Achievement Award. in wireess mobie networks, in IEEE INFOLiusheng Huang is a professor at the COM, 27. Schoo of Computer Science and Technoogy C. Liu and J. Wu, An optima probabiistic forin University of Science and Technoogy of warding protoco in deay toerant networks, in China. He received his M.S. degree in computer science from University of Science and ACM MobiHoc, 29. Technoogy of China in He serves on T. Spyropouos, K. Psounis, and C. S. Raghaventhe editoria board of many journas. He has dra, Efficient routing in intermittenty conpubished 6 books and more than 2 papers. His main research interests incude denected mobie networks: the singe-copy case, ay toerant networks and Internet of things