Maximizing Timely Content Advertising in DTNs

Transcription

1 Maxmzng Tmely Content Advertsng n DTs Wexong Rao, Ka Zhao, Yan Zhang, Pan Hu and Sasu Tarkoma Department of Computer Scence Smula Research Laboratory Deutsche Telekom Laboratores Unversty of Helsnk, Fnland orway Germany {frstname.lastname}@cs.helsnk.f yanzhang@smula.no pan.hu@telekom.de Abstract Many applcatons, such as product promoton advertsement and traffc congeston notfcaton, beneft from the opportunstc content exchange n Delay Tolerant etworks (DTs). An mportant requrement of such applcatons s tmely delvery. However, the ntermttent connectvty of DTs may sgnfcantly delay content exchange and cannot guarantee tmely delvery. The state-of-the-arts capture the moblty patterns or socal propertes of moble devces. However, there s lttle optmzaton n terms of the delvered content. Wthout such optmzaton, the content demanded by a large number of subscrbers could follow the same forwardng path as the content by only one subscrber. To address the challenge, n ths paper, we separate content routng from content forwardng. For content routng, we leverage content propertes to derve an optmal routng hop count for each content n order to maxmze the number of nodes whch receve demanded content. ext, for tmely forwardng, we develop node utltes to capture nterests and moblty patterns of moble devces for the selecton of content carrers. The dstrbuted greedy relay scheme,, leverages the optmal routng hop count and developed utltes to tmely relay content to the needed nodes as fast as possble. Illustratve results show that s able to acheve comparable delvery rato as the Epdemc but wth much lower overhead. I. Introducton In Delay Tolerant etworks (DTs), whenever moble devces (PDAs, vehcles, moble phones, etc.) encounter each other, they exchange content va short-range communcatons (e.g., Bluetooth or WF). Thus, many applcatons and servces, such as product promoton advertsement and traffc congeston notfcaton, beneft from the opportunstc content exchange. It s useful n the areas where wreless networks do not cover, wreless access s blocked, or cellular networks are congested [1]. Opportunstc communcaton thus helps expandng the network coverage, wthout buldng dedcated network nfrastructures. An mportant requrement assocated wth exchanged content s freshness. That s, besdes delverng the content towards the needed users, we further expect the content to be tmely delvered. For example, tmely delvery of certan product promoton news can be crtcal, e.g., at least before the end day of the product promoton perod. Otherwse, outdated content, though delvered, s meanngless to users. However, opportunstc delvery fashon essentally conflcts the freshness requrement. Servce provders expect to maxmze the number of potental users who can tmely receve content, and hence the tems must be delvered n tme. On the other hand, due to the ntermttent connectvty of DTs, The last author s also afflated wth Department of Computer Scence and Engneerng, Aalto Unversty, Fnland the opportunstc exchange may experence certan delay, and cannot guarantee an expected delvery delay [4]. In ths paper, we study the problem of maxmzng the number of users who can tmely receve content. In detal, we are nspred by the topc-based model [6] to offer personalzed content subscrpton. Ths model s wdely used n many real applcatons (e.g., RSS feeds, onlne games). Subscrbers declare ther nterests by specfyng topcs nsde subscrpton condtons (called flters). An advertsement (whch precsely means a content tem n ths paper) s assocated wth a topc. An advertsement matches a flter (or a flter matches an advertsement), f and only f both the advertsement and flter contan the same topc. The state-of-the-arts [7], [11], [15], [17] leveraged moblty patterns or socal propertes of moble devces to select forwardng paths. However, there s lttle optmzaton n terms of the delvered content. Wthout such optmzaton, the content demanded by a large number of subscrbers could follow the same forwardng path as the (same) content demanded by only one subscrber. It s because the prevous work manly leveraged on the propertes of moble devces, nstead on the content propertes, to optmze the overall content routng. Real applcatons show many unque content propertes, such as correlaton between content supples and demands [16], the well-known Zpf dstrbuton [2]. Based on these content propertes, we propose a new content relay scheme, namely. Specally, dfferng from the above work, shares some smlar dea to the contentcentrc networkng [12], [13], [14]. It separates the end-toend routng (from publshers to subscrbers) from the pontto-pont forwardng among encountered nodes. After revewng related works (Secton II), we defnes the problem and hghlghts the soluton (Secton III), and make the followng contrbutons to support the novel dea of separatng the content routng from content forwardng: We develop an optmal strategy to desgn an optmal hop count for each routed content. The content wth such routng hops s expected to reach the needed nodes (Secton IV). By leveragng the developed utltes to capture the nterests and moblty patterns of moble devces (Secton V), we desgn an adaptve algorthm to select the best carrers for tmely forwardng (Secton VI). We extensvely evaluate the effcency of the over two realstc data sets and verfy that s able to acheve comparable delvery rato as the Epdemc but wth much lower overhead (Secton VII).

2 II. Related Work In the context of DT, [23] studed Epdemc routng by selectng all nodes n the network as relays. ProPHET [15] leveraged encounter hstory to predct the delvery possblty. [22] sprayed data to relays watng for contacts wth destnatons. [1] leveraged a Markovan model to develop an effcent utlty functon for content dssemnaton. [3] used the path lkelhoods to schedule packets transmtted to other peers and packets to be dropped. These works focused on capturng moblty patterns of moble devces, and all desgned for oneto-one routng. Recent works[7],[9],[11],[17] took advantage of socal behavors of moble devces to dentfy the best nformaton carrer. These works exploted socal propertes (e.g., centralty,) to support the one-to-one routng [11], [17], [3], and one-to-many routng [7], [9]. Dfferng from these works, we observe that content propertes could optmze content delvery and desgn an optmal routng hop count for each routed content. In terms of utltes for the selecton of carrers, [7], [11], [9] manly used the utltes to predct the delvery possblty of moble devces. Dfferng from these works, the man purpose of our developed utltes s to capture the nterests of moble devce (together wth ther moblty patterns). For the detals to compute the utltes, [7] dd not adopt an accumulatve utlty functon. Though havng the cumulatve contact length as edge weghts n socal networks, [11] dd not leverage such weghts for data forwardng, and [9] used the same utltes for varous content tems. Instead, our proposed utltes ncorporate the self-nterest of a specfc node and overall nterests of the whole DT, and develop a specfc utlty for each topc. In content-centrc networkng [12], [13], a communcaton network allows a user to focus on the data he or she needs, rather than havng to reference a specfc, physcal locaton where that data s to be retreved from. Dfferng from such workswththevsonforacleanslatedesgnoffutureinternet, we leverage content propertes to derve an optmal routng hop count. In addton, the prevous works [19], [] shared some smlar dea to proactvely assgn more resources (such as replcas) for popular content, but were desgned for P2P networks. III. Problem Statement and Soluton Overvew We expect DTs as complementary network communcaton technologes [1]. They help content provders delver the content (generated by the content provders) to the needed nodes and explore more potental customers. Suppose that the opportunstcally encountered devces are connected as a DT. The roles of moble devces can be publshers, subscrbers or carrers. Publshers publsh advertsements d of specfc topcs t. Subscrbers regster subscrpton flters (contanng defned topcs t ) to expect the advertsements of t. In addton to publshers and subscrbers, moble devces can act as carrers to relay advertsements. When moble devces encounter each other, the carred advertsements are then exchanged, and fnally relayed from the publshers to the subscrbers wth the help of ntermedate carrers. Due to the dverse advertsements and nterests, publshers and subscrbers defne ther favorte topcs. Suppose there exst a total number of T topcs. For a specfc topc t (1 T), we assume that nodes are nterested n t (f a node regsters a flter contanng t, we say that the node s nterested n t ). We defne the demand rate p of a topc t to be the rato between and,.e. p = /. Let M denote the total number of advertsements. We next defne the supply rate q wth respect to (w.r.t) a topc t, and thus q M advertsements are assocated wth t. Gven the above notatons, we defne the followng problem: Problem 1 Wthn a gven tme perod P, we want to desgn an advertsement relay scheme to maxmze the number of nodes whch can receve the matchng advertsements. In Problem 1, an advertsement matches a node f the node regsters a flter havng the same topcs as the advertsement. Gven Problem 1, our basc dea s to separate content routng from content forwardng. For content routng, we leverage content propertes to desgn an optmal hop count for each routed content. ext, for content forwardng, we develop the node utltes to capture nterests and moblty patterns of moble devces. Then the content forwardng leverages the utltes to select the best carrers for routed content. In detal, n Secton IV, for each advertsement d (wth a topc t ), develops an optmal number X of opportunstc encounters for d. Intutvely, the optmal number X can be treated as the overall routng hop count to route d from publshers to subscrbers. That s, when creates only one copy for d, X s the number of hops (or TTL) to route the d towards the needed nodes. When creates multple copes of some d ( d ), X s the accumulatve number of hops to route all copes of the d. Thus, adaptvely allows ether the uncast (e.g., for d ) or multcast (e.g., for d ) to maxmze tmely content advertsng. The key of s to leverage the content propertes and proactvely assgn more hop count for popular advertsements whch are hghly demanded by a large number of subscrbers. Thus, more nodes act as the carrers to route the popular advertsements, and subscrbers tmely receve the needed advertsements. ote that the developed X n Secton IV does not consder moblty patterns of DT nodes. Thus, Secton V desgns the utltes to capture the moblty patterns and nterests of moble devces. Then, based on the utlty of each node, selects the best carrer for each d to tmely forward d towards the needed nodes. Specfcally, we use a vector U j to represent the utltes of a node n j. Gven T topcs, U j contans T elements. For a topc t (1 T), the element u j U j represents how good the node n j can successfully relay the advertsements wth the topc t to the needed nodes. The vector U j and the element u j are named as the vector utlty and an element utlty, respectvely. Based on the element utltes, can dentfy () the nodes that are nterested n the topc t and () how fast the encountered node can tmely forward d to the needed nodes.

3 Symbol T M p q d H X H X Meanng Total number of topcs Total number of advertsements Total number of nodes n DT Demandng rate of a topc t (1 T) Supplyng rate of a topc t (1 T) An advertsement assocated wth a topc t (1 T) the set of nodes nterested n t, wth the cardnalty umber of nodes whch can successfully receve d umber of requred encounters to relay d to the needed nodes Total number of nodes whch receve matchng advertsements Total number of opportunstc encounters to relay advertsements TABLE I Meanngs of man symbols used Gven the above two technques, n Secton VI, selects the best carrers of each advertsement, such that an advertsementd andtscopesexperence X encountersasfast as possble. We prove that the problem of selectng the best carrers to relay advertsements s P-hard. Then, we propose the algorthm detals of. IV. Optmal Advertsement Relay Strategy We frst hghlght the general dea as follows. We defne the event that two nodes encounter as an encounter event, no matter moblty pattern and socal propertes of moble devces. For example, gven three nodes n j, n j and n j, frst n j encounters n j after 1 day, and then n j encounters n j after only 1 mnute. The two occurred events are treated equally, because the occurrence of such events depends upon whether or not two nodes encounter, rather than the experenced perod or encounter frequency. Based on the encounter events, we derve a functon f( ) between the needed encounters to relay an advertsement and the expectaton of the number of nodes whch can successfully receve the matchng advertsements (Secton IV-A). ext, consderng the overall advertsements, we develop a strategy to ensure that each advertsement experences an optmal number of encounters, such that we can maxmze the total number of nodes whch can successfully receve matchng advertsements (Secton IV-B). Essentally, the technques of ths secton are to explot the propertes of advertsements (.e., the demandng and supplyng rates), and do not consder the effect of moblty pattern of moble devces. Such patterns are consdered by the developed utltes for the selecton of carrers (Secton V). Table I summarzes the man symbols used n ths secton. A. Probablstc Advertsement Relay Gven an advertsement d wth a topc t, we denote to be the set of the nodes that expect the advertsement d (.e., = p s the cardnalty of ). For a specfc encounter event among all encounter events, we compute the probabltyρ that the encounter successfully relays an advertsement d to a node nsde. Suppose a node carryng d s opportunstcally encounterng another node, whch could be a member node nsde or not. Among the nodes n the DT, nodes are the members of. Thus, the average probabltyρ s, because () the defned encounter events depend only upon whether or not nodes encounter, nstead of the moblty patterns and socal propertes of moble devces and ()ρ now depends only upon the dstrbuton of flters among the nodes of DT. Based on the above analyss, the probabltyρ 1 of a specfc encounter to relay d to the frst new node nsde s, because any node nsde could be the node to receve d. ext, the probabltyρ 2 that a specfc encounter successfullyrelaysd tothesecond newnoden s (1 1 ),where () s the probablty of a specfc encounter to successfully relay d to any node nsde and () (1 1 ) s the probablty that among the nodes, any of those nodes (except the frst new node) receves d. The reducton of 1/ s to elmnate the stuaton that d s duplcately forwarded to the frst new node that has already receved d. Smlarly, the probablty ρ j that a specfc encounter to successfully relay d to the j-th new node nsde s ρ= j j 1 (1 ) (1) In Equaton (1), the tem (1 j 1 ) represents the probablty that any of the nodes nsde the set (except the prevous (j 1) nodes) can receve the advertsement. Gven the probabltyρ j, the tral that a specfc encounter successfully relays d to the j-th new node nsde can be treated as a geometrc probablty dstrbuton wth the parameterρ j. Thus, the expected number of opportunstc encounters needed to successfully relay d to the j-th new node s X j = 1 ρ j = j+1 = j+1 Suppose our advertsement relay strategy wll ensure that d experences X opportunstc encounters towards the nodes n. We are nterested n the number of nodes n that can successfully receve d. Let H denote the number of nodes n that can successfully receve d. Then, gven the number X, we compute H as follows: H H X j = j=1 j=1 j+1 = X (3) For Equaton (3), we make the followng transformaton: H j=1 j+1 = 1 H j j=1 j=1 1 j (2) ln H (4) The above transformaton (wth H < ) utlzes the result that the summaton 1 j=1 j,.e., the harmonc number, s approxmated by ln. Smlar reasonng apples for H 1 j=1 j and t s approxmated by ln( H ). Consequently, we can derve the functon f( ) between H and X as follows: Theorem 1 If our relay strategy ensures that an advertsement d assocated wth t can experence X opportunstc encounters,wehavethefunctonbetween ( H and X asfollows. H = p 1 e X ). Proof: Based on Equatons (2-4), we obtan X = ln H, and then valdate the correctness of the theorem. In case of X = log, we have H =.

4 B. Optmal Relay Strategy In ths subsecton, consderng the overall advertsements assocated wth T topcs, we develop an optmal relay strategy to maxmze the total number of nodes whch can successfully receve matchng advertsements. By Theorem 1, f an advertsement d experences X opportunstc encounters, H nodes can successfully receve d. We consder the effect of the supplyng rate q as follows. Suppose that among all of the M dstnct advertsements, the topc t s suppled wth q M advertsements. When such advertsements are ndependently publshed by publshers, by q M X opportunstc encounters, q M H nodes can successfully receve matchng advertsements. Gven the total T topcs, the number of nodes whch receve the matchng advertsements, denoted as H, s computed by: H= T [ ] T [ ] q M H = M q p (1 e X ) =1 On the other hand, moble devces opportunstcally encounter each other, and the occurrence of the content exchange depends on whether or not such devces encounter. Therefore, the overall opportunstc encounters to relay advertsements are decded by the moblty pattern of moble devces (and other parameters lke battery, etc.). Thus, wthn a gven tme perod P, the total number of such opportunstc encounters s a gven number X. Hence, we consder that the constrant that the total number of encounters,.e., T =1 (q M X ), s assocated wth at most X encounters. Formally, gven the optmzaton problem to maxmze the H n Equaton (5) wth the constrant T =1 (q M X )=X, we have the followng theorem: Theorem 2 Gventheconstrant T =1 (q M X )=X,thetotal number H of nodes recevng the matchng advertsements s maxmzed when X = X M +lnp T =1 (q lnp ). To prove Theorem 2, we leverage the Lagrange multpler method to obtan the optmal X n terms of p and q. Due to the space lmt, we skp the detals of such proof. We refer nterested readers to the techncal report [21] for the detals. Based on Theorem 2, we have the followng dscusson. When p s larger,.e., more nodes are nterested n t, the tem lnp s a smaller negatve value, thus resultng n a larger X. In terms of physcal nterpretaton, f d s demanded by more nodes, the relay strategy should ensure that more nodes act as the carrers to relay d, and the nodes carryng d encounter more nodes n. When X,M and are gven, X depends on the dstrbuton of p and q. When the dstrbuton of p and q s more skewed, T =1 (q lnp ) and X become smaller. Ths means that the skewed dstrbuton functons of p and q help use smaller X to relay advertsements to the nodes. Many real applcatons ndcate a skewed dstrbuton of p and q [18], [6], whch favors the optmzaton strategy. =1 (5) The soluton to the optmzaton problem n Theorem 2 needs to know the values of the parameters p, q, etc, whch can be acqured by content provders as follows. Frst, snce the content s generated by content provders, the provders can easly compute the parameters (e.g., q, etc.) w.r.t. the content. To compute the parameters (e.g., p, etc.) w.r.t. flters, subscrbers can be requred to regster subscrpton flters to the regstraton server hosted by the content provders(that s possble because we expect that the DT s as a complementary network communcaton technologes). Besdes, the dstrbuted soluton,e.g.,[11],helpsapproxmatetheparameters p andq. Fnally, for the content wth low p but requred to be urgently delvered to the needed nodes (such as the alarm of urgent events), we assgn the content wth a hgh prorty. Then, the content s not evcted by the buffer manager (whch uses the least recent used (LRU) polcy to evct expred tems) and s tmely relayed to the encountered nodes. V. Relay Utltes In ths secton, we gve the detals of the developed utltes, whch capture the subscrpton nterests and moblty pattern of moble devces, for the selecton of node carrers. A. Data Structure For a node n j, we use a vector U j (called vector utlty) to represent n j s utltes. To capture moble devces nterests, U j contans T elements (due to the exstence of T topcs), and each element s assocated wth a topc. The element u j U j (1 T), called element utlty, ndcates the goodness of n j to successfully relay an advertsement d (wth a topc t ) to the nodes n. A larger u j ndcates that n j has more chance to successfully relay d to the nodes n. The proposed utltes have two unque propertes to capture the nterests of moble devces. Among all elements n U j, the one wth the largest value s assocated wth the topc t that node n j tself s nterested n. Thus, f the utlty U j s avalable to a thrd node n k, by dentfyng the largest element nsde U j, n k then dentfes that n j s nterested n the topc assocated wth such an element, before n k communcates wth n j. Ths property s useful for to tmely relay d towards the needed nodes. Except the element wth a largest value, the remanng elements n U j accumulate the nterests of the whole nodes n the DT. That s, f a topc t s popularly regstered n many nodes of DT, the assocated element s larger. In addton, the utlty U j ncorporates the moblty pattern (e.g., encounterng rate) of n j. In Fgure 1, the leftmost column shows the utlty vector of a node n 1. For the 4 topcs t A...t D, n 1 s assumed to be nterested n t A. Thus, the element of t A has the largest value.614, ndcatng that n 1 s self nterested n t A. In addton, snce t B s popularly regstered n 3 other nodes (n 2,n 3 and n 4 ), the assocated element utlty,.271, s also larger than the two remanng element utltes (.e.,.71 and.42). In detal, for a specfc topc t, the element utlty u j has consdered the followng cases. () The node n j tself s

5 Fg. 1. An example to compute the utltes of n 1 for 4 topcs t A...t D nterested n t, and () n j, though not nterested n t, can act as the carrer of d to successfully relay d towards. Therefore, we need the followng nformaton to compute u j. For the nterest of the node n j tself, we use a /1 vector oft elementsr j to represent ts own nterest. The element r j pertanng to t s equal to 1 (.e., r= j 1), ff the node n j s regstered wth a flter defnng t. The utltes U k of the nodes (say n k ) that n j prevously encountered wthn a specfc perod P. U k (resp. U j ) s avalable to n k (resp. n j ) by exchangng the utltes when n j and n k encounter each other. The encounterng rate f j,k of two moble devces n j and n k. The value of f j,k captures the frequency that n j and n k ever encountered (note that f j,k can be adapted by consderng the other aspects of n j and n k, such as the battery level, socal propertes and network bandwdth). In Fgure 1, the 2nd leftmost column ndcates the /1 vector n terms of n 1 s self-nterest: the element pertanng to t A s 1 becausen 1 snterestednthetopct A.Thethreecolumnsfrom the 3rd leftmost column to the rghtmost column n Fgure 1 show the utltes of 3 prevously encountered nodes n 2, n 3 and n 4, respectvely. The tems above the three columns show the encounterng frequency (.e., 1, 4, and 2) between n 1 and the three nodes nsde a perod. Followng [7], the nodes that ever frequently encountered have hgh chance to encounter agan n the future. Thus, f j,k helps predct the chance that n j and n k wll encounter each other. More other technques (e.g., by leveragng spatal and socal propertes) can be ncorporated for further mprovement. Though the computaton of the vector utlty U j does need all above tems, the followng subsecton wll show that t s unnecessary for n j to mantan u k and f j,k for all prevously encounterednodesn k.thus,weavodtheexpensve mantenance overhead, partcularly when n j encountered a large number of nodes. B. Detals to compute utltes Suppose that n j prevously encountered K nodes n k (1 k K) nsde a wndow (e.g., a sldng wndow of 6 hours). To compute U j, the accumulaton technque captures the overall nterests of the whole DT, and the normalzaton technque captures the self-nterests of n j. In detal, the node n j uses the followng four steps to compute U j. (1) Overall Accumulaton: For all of these K nodes n k that n j encounters, we compute the overall utlty U () j and ts element u () j. For an element u () j n terms of a topc t, we accumulate u () j = K k=1 (f j,k u k ) for all such nodes n k. For example, n Fgure 1, we compute u () j for the topc t A as 1.6 (= ). Smlarly, we can compute the overall element utltes for other 3 topcs t B, t C and t D as 3.8, 1. and.5, respectvely. (2) Overall ormalzaton: We normalze the utlty U () j to U() j by computng the element u() j = u () j / T =1 u () j. Followng the above example, for a topc t A, ts normalzed overall utlty s 1.6/( )=1.6/7.. (3) Self Accumulaton: Based on the normalzed overall utlty U() j and the self-nterest r j, we compute the utlty U j by settng ts element u j to u j r = j +u()j j T=1 r j +u()j T=1 r j + T =1 u() j = r +1.. For example for t A, u j t A = 1+1.6/ (4) Self ormalzaton: we fnally normalze the utlty U j to U j by u= j u j / T =1 u j (e.g., for t A, u j t A =.614). Durng the above steps, step 1 accumulates the utltes of the prevously encountered nodes n k to capture the overall nterests of the nodes n k, such that n j acts as the carrer to relay d from n k towards the nodes ntermedately gong through n j. ext, step 3 accumulates the self-nterests of n j wth the overall utltes. Thus, the accumulaton ensures that U j can measure the goodness to relay d towards n j tself and other nterested nodes. In addton, gven the self-nterests wth r j = 1, the normalzaton of steps 2 and 4 ensures that among all elements n U j, the element u j s assocated wth the largest value. Ths property helps relay the advertsement d towards those nodes n va the greedy polcy n the proposed scheme. As mentoned prevously, t s unnecessary to mantan the u k and f j,k for all prevously encountered nodes n k. Instead, we only mantan the accumulated overall utlty U () j (see the above step 1). When n j encounters a new node n k, the element u () j of U () j s ncrementally updated by u () j = u () j +u k. After that, we stll follow the above steps 2-4 to renew the utlty U j. Therefore, the node n j only needs to mantan the overall utlty U () j, the self-nterests r j, and the fnal utlty U j, and the assocated mantenance cost s low. VI. Dstrbuted Greedy Relay Scheme Gven the assgned opportunstc encounters X (gven by Theorem 2 of Secton IV), we develop a dstrbuted relay algorthm,, whch leverages the developed utltes to select the best nodes as the carres of d. A. Two Basc Solutons Before presentng the proposed relay algorthm, we frst gve two basc solutons. Snce Theorem 2 assgns X encounters for the advertsement d, we ntutvely consder that the advertsement d (and ts copes, f have) s assocated wth an overall TTL equal to X. Suppose that the ntal publsher node n 1 starts the relay of d. The frst basc soluton, namely broadcast, s shown as follows. Whenever the ntal node n 1 encounters a node n 2, d s coped to the node n 2. If n 2 regsters a flter f matchng d, then d s successfully dssemnated to the needed node. After that, both n 1 and n 2 reman the copes of d and act as the carrers of d. Meanwhle, such two copes of d 2 are assocated wth a new TTL, whch s equal to (X 1)/2. If n 1 and n 2 encounter more other nodes, d s smlarly coped

6 and the assocated TTLs are renewed. The relay of d (and ts copy) s stopped when the current TTL s equal to. Second, based on the uncast soluton, when n 1 encounters n 2, d s relay from n 1 to n 2 f the element utlty u 2 s larger than u 1 ; meanwhle, n 1 does not reman a copy of d. Then, n 2 acts as the unque carrer of d wth a new TTL (X 1). When n 2 encounters a thrd node n 3, f u 3 > u 2, then d s relayed to n 3 assocated wth the new TTL (X 2). As before, the uncast s fnshed when the current TTL s equal to. Dfferent from the broadcast scheme, the uncast scheme has only one copy of d durng the whole relay process. The above broadcast and uncast schemes suffer from dsadvantages. Frst, the broadcast ncurs too many copes of advertsements. Due to a lmted buffer sze n each node, too many copes of advertsements ncur the overflow ssue and evct useful advertsements (we use the least recent used (LRU) polcy to evct the advertsements). On the other hand, though avodng the overflow ssue, the uncast ncurs a hgh latency before d s successfully relayed to the expected nodes. Thehghlatencymaybeevenlargerthanthegventmeperod P, and the advertsement becomes expred. In ths secton, the scheme combnes the benefts of the uncast and broadcast schemes, and relay (ether broacast or uncast) advertsements towards the needed nodes. Dependng on the utltes of encountered nodes, the leverages the developed utltes to select the best carrers, and adaptvely adjusts the number of advertsement copes to tmely delver the advertsement to the needed nodes as fast as possble. B. Problem Statement We model the DT as an opportunstc graph G. Each node n j (1 j ) n DT s represented by a correspondng vertex n G. If the node n j opportunstcally encounters a node n k ( n j ), there s an edge between n j and n k. In the graph G, each node n j s assocated wth a utlty vector U j, and each element utlty u j n the vector U j represents the utlty of n j to relay the advertsement d. The weght assocated wth the edge between n j and n k depends upon the element utlty u j and the encounterng frequency f j,k between two nodes n j and n k. Larger values of u j and f j,k ndcate hgher chance of n j to successfully relay d from n j to n k (and vce versa). Thus, we can desgnate that the edge between n j and n k wth a weght (f j,k u j ). We formulate the followng problem. Problem 2 Gven an opportunstc graph G, we want to fnd X connected edges startng from n j, such that the sum of all such edges are maxmzed. The optmzaton problem to maxmze the sum of X connected edges of flters s harder than ts decson problem. Ifasolutonoftheoptmzatonproblemsknown,wecanfnd the vertces whch are the endponts of such edges. Then, by smplycountngthenumberofnodesthatappearn,wecan compare the number of such nodes wth the gven number H. We can prove that Problem 2 s P-hard by reducng t from the classc set cover problem. Therefore, we gve a heurstc algorthm as follows. C. A Dstrbuted Heurstc Soluton Snce no node n DT knows the global opportunstc graph G, we can not drectly apply the classcal greedy algorthm of the set cover problem. We nstead propose a dstrbuted greedy-based heurstc algorthm,, to select the best nodesndttotmelyrelaytheadvertsementd.wesuppose that the relay of d starts from an ntal node n j. Algorthm 1: Relay Selecton nput : ode n j, carryng d, s opportunstcally encounterng node n k 1 n j (resp. n k ) updates U j (resp. U k ) by exchangng utltes wth n k (resp. n j ); 2 f n k s nterested n d then d s forwarded to n k ; 3 f the element utlty u k s larger than the element utlty u j then 4 n k keeps a copy of d ; 5 f u k >µ j // /*µ j s the largest element utlty of the topc t among all nodes that n j ever encountered*/ 6 then n j removes d ; 7 else n k does not keep a copy of d ; As shown n Algorthm 1, the two encounterng nodes n j and n k exchange and update ther utltes U j and U k (Secton V has already gven the detals to compute the utltes). ext, when the node n j s nterested n d, then d s coped from t to n k. After that, n k receves the matchng advertsement d. In lne 3, f the element utlty u k of n k n terms of the topc t s larger than the element utlty u j of n j n terms of t, then n k keeps a copy of d n the buffer (lne 4). Otherwse, n j wll not keep a copy of d (lne 7), f one of the followng cases occurs: () n j s nterested n t but n k not, ndcatng that u k < u j must hold, () nether n j nor n k s nterested n t, but u k < u j holds, and () both n j and n k are nterested n t, but u k < u j holds. It means that even f lne 2 s executed, n k stll removes d (lne 7). Ths makes sense because n j s better than n k to act as the carrer of d (e.g., n k s nterested n t but none of ts prevously encountered nodes s nterested n t. Thus t s meanngless for n k to act as the carrer). In lnes 5-6, there s another opton whether or not n j stll needs to keep a copy of d n the buffer and acts as the carrer of d. If u k s larger thanµ j,.e., the largest utlty of the topc t among all nodes that n j ever encountered, then n j removes d from ts buffer and wll not act as the carrer of d. Otherwse, n j stllkeepsd ntsbufferandactsasthecarrerofd.durng the encounter between n j and n k,µ j s updated f u k s larger than the currentµ j. In addton, Algorthm 1 updates the TTL of d as follows. Suppose that the current TTL assocated wth the advertsement d s X (X s ntally equal to X ). If both n j and n k keep the copes of d n ther local buffers, the new TTLs assocated wth both copes are set by (X 1)/2. Otherwse, f ether n j or n k keeps a sngle copy of d, the new TTL assocated wth such a copy s (X 1). The relay of a copy of d s termnated f the assocated TTL s zero. Based on Algorthm 1, those nodes havng larger utltes u j are selected as the carrers of d, and d s greedly relayed to the nodes wth larger element utltes. The greedy polcy helpsrelayd tothenodesn asfastaspossble.inaddton, Algorthm 1 follows the dea of broadcast to allow multple

7 copes of d, and thus ncreases the delvery rato. Algorthm 1 also follows the dea of uncast to lmt the number of such copes n lnes 3-6, and avods creatng too many copes. Our experment shows that Algorthm 1 effcently delvers d towards the needed nodes wth hgh delvery rato and sgnfcantly low overhead. VII. Evaluaton A. Expermental Settngs We compare the scheme wth the Epdemc scheme [23] (.e., the floodng-based approach), ProPHET [15] (.e., the probablstc approach), and Bubble Rap (.e., socal aware approach). ote that for Bubble Rap, when a content tem s needed by multple subscrbes and such subscrbers are located at multple communtes, we then have to forward the tem to all such communtes. In addton, we also compare the scheme wth the broadcast and uncast schemes havng the optmal encounters, both of whch are gven n Secton VI-A. We use two real-world datasets of human moblty traces to run our smulaton. The Infocom6 dataset [5] contans opportunstc Bluetooth contacts between 98 Motes, 78 of whch were dstrbuted to Infocom6 partcpants and of whch were statc. The MIT Realty trace [8] comprses 95 partcpants carryng GSM enabled cell-phones over a perod of 9 months. We consder, as n [5], that two phones are n contact when they share the same GSM base staton. ext, followng the prevous works [6], we use the Zpf dstrbuton to generate flters and content tems for a set of gven topcs. To select subscrbers, we ensure that each node regsters a flter and thus the number of subscrbers (and the number of flters) s equal to the node count. ext, we randomly choose the publshers from all nodes. Table II shows the parameters used n the experments. Takng the Zpf parameterαas an example,.95 s the default value and the nterval [.,1.2] s the allowable range. In addton, we are nterested whether or not the skew of flter dstrbuton correlates the skew of content popularty. The correlaton means that a topc, whch s hghly demanded by subscrbers, smultaneously popularly appears n content tems. Otherwse, the skew of both dstrbutons s antcorrelated. By default, we set up the correlated topcs to generate flters and content (wth the Zpf dstrbuton). Parameter Infocom6 MIT Realty num. of topcs 1 1 num. of flters num. of content tems buf. sze per node 3: [5-] :[5-] runnng perod P 5: [1-8] mns 21:[1-9] days Zpf parameter α.95: [.-1.2].95: [.-1.2] TABLE II Parameters for Dgg Experments Fnally, we use the followng metrcs to measure the performance of our smulatons. () Delvery rato: the average rato of the number of delvered destnatons to the total number of destnatons. () Average delay: the average delay for all the delvered destnatons to receve the data. () Average cost: the average number of content transmssons (ncludng transmssons for duplcated copes) used to delver a data tem. Thus, the average cost measures the average overhead to delver the data tem. The duplcated copes are shown as follows. Snce the topc-based model s essentally a many-tomany communcaton manner (one topc s assocated wth multple content tems and multple subscrbers), a content tem, after arrvng at a subscrber node, stll needs to be forwarded to the remanng subscrbers. As a result, a content tem could duplcatedly reaches the same relay nodes. It s partcularly true when exstng content tems are evcted due to the lmted buffer sze (we use a LRU evcton polcy). B. Effect of Tme Perod Frst, n Fgure 2, we study the effect of the allowable tme perod P over the Infocom6 and MIT realty traces. As shown n Fgure 2 (a), among the four schemes, the scheme acheves comparable delvery rato as the Epdemc scheme, the Bubble Rap scheme has a lower delvery rato than, and the ProPHET scheme has the least delvery rato. In partcular, a larger tme perod P, varyng from 1 mnute to 8 mnutes, leads to a larger delvery rato. Ths s due to the sparse DT property and the low encounterng rate of node contacts. A larger P ndcates that more nodes have chance to relay content tems towards the needed nodes, and thus the delvery ratos of all four schemes ncrease accordngly. Second, Fgure 2 (b) plots the average delay. Result ndcates that the scheme uses a comparable low delay as the Epdemc scheme to delver content tems towards needed nodes. It s because the developed optmzaton strategy can help optmze the delvery of hghly demanded content by usng more nodes as carrers, and then content tems are delvered as fast as possble. ext for the average cost, Fgure 2 (c) shows that the scheme uses a sgnfcantly low cost. For example, when P=8 mnutes, the average cost of the scheme s 3.5% of the Epdemc scheme, 5.22% of the Bubble Rap scheme, and 1.3% of the ProPHET scheme, respectvely. These results ndcate the hgh effcency of the scheme. The low cost of s manly because gven the skewed popularty dstrbuton α =.95, proactvely assgns more optmal encounters for popular tems, but meanwhle assgns fewer encounters for unpopular tems. Furthermore, the relay algorthm of lmts the copes of content tems and thus lmts the content transmssons. For Bubble Rap, snce a content tem mght be located at multple communtes, the tem has to be forwarded to all such communtes, leadng to the cost of Bubble Rap close to the Epdemc approach. In addton, the average cost shown n ths fgure s even larger than the number of devces (98 motes for Infocom6 data set). It s because duplcate content tems reach the same relay nodes (caused by the many-to-many topc model and LRU evcton polcy for the lmted buffer sze). Smlar stuaton occurs for other results for the average cost. When we compare Fgures 2 (a-c) wth Fgures 2 (d-e), the nodes n the MIT realty trace have to use a longer tme perod than the nodes n the Infocom6 trace, untl the almost same delvery rato (for example, %) s acheved. It s

8 Delvery rato (%) Epdemc ProPHET 1 1 Tme Perod (mns) Average delay (secs) 1 1 Epdemc 1 1 Tme Perod (mns) 1 1 Epdemc 1 1 Tme Perod (mns) Delvery rato (%) Epdemc Tme Perod (days) Average delay (hours) Epdemc Tme Perod (days) Epdemc Tme Perod (days) (a) Delvery Rato (IFO6) (b) Average Latency (IFO6) (c) (IFO6) (d) Delvery Rato (Realty) (e) Average Latency(Realty) (f) (Realty) Fg. 2. Effect of the tme perod P on the Infocom6 and MIT Realty data traces Delvery rato (%) Epdemc Buffer sze Average delay (secs) 15 5 Epdemc Buffer sze Epdemc Buffer sze Delvery rato (%) Epdemc Buffer sze Average delay (hours) Epdemc Buffer sze 15 5 Epdemc (a) Delvery Rato (IFO6) (b) Average Latency (IFO6) (c) (IFO6) (d) Delvery Rato (Realty) (e) Average Latency(Realty) (f) (Realty) Fg. 3. Effect of the buffer sze S on the Infocom6 and MIT Realty data traces Buffer sze Delvery rato (%) Epdemc Zpf parameter Average delay (secs) 15 5 Epdemc Zpf parameter Epdemc Zpf parameter Delvery rato (%) Epdemc Zpf parameter Average delay (secs) Epdemc Zpf parameter 15 5 Epdemc Zpf parameter (a) Delvery Rato (IFO6) (b) Average Latency (IFO6) (c) (IFO6) (d) Delvery Rato (Realty) (e) Average Latency(Realty) (f) (Realty) Fg. 4. Effect of the Zpf Parameter on the Infocom6 and MIT Realty data traces Delvery rato (%) Uncast Average Delay(secs) Uncast Uncast Delvery Rato Uncast Average Delay(hours) Uncast Uncast ant-relaton co-relaton ant-relaton co-relaton ant-relaton co-relaton ant-relaton co-relaton ant-relaton co-relaton ant-relaton co-relaton (a) Delvery Rato (IFO6) (b) Average Latency (IFO6) (c) (IFO6) (d) Delvery Rato (Realty) (e) Average Latency(Realty) (f) (Realty) Fg. 5. Comparson of Three Schemes because the encounterng rates of the parwse nodes n the MIT realty trace are much lower than those n the Infocom6 trace. evertheless, consstent wth Fgure 2 (c), the scheme n Fgure 2 (e) uses the least average cost. C. Effect of Buffer Sze In ths experment, we vary the buffer sze S per node (gven the sze S, when more content tems come at the node, the old tems are evcted by the FIFO manner), and study the performance of four schemes n Fgure 3. In general, a larger S helps acheve hgher delvery ratos for all four schemes. Among the four schemes, the Epdemc scheme obvously benefts most from a larger S, because the Epdemc scheme creates the largest number of copes of content tems to be propagated across nodes. Smlar to the Epdemc and Bubble Rap schemes, the scheme allows more copes of popular content tems, and benefts from a larger S. Instead, the ProPHET scheme benefts least from a larger S. A larger S does not necessarly lead to a smaller average delay and cost. In Fgure 3 (c), only after S s suffcent large, the average cost of the Epdemc scheme becomes smaller. Ths s because the average cost depends on both the number of delvered advertsements to the needed nodes and the number of used relays. Though a larger S does ncrease the number of delvered tems, t also leads to a larger number of relays. After P s suffcent large, the number of delvered tems becomes enough large to ensure that the average cost s smaller. Such trend consstently appears n both Fgure 3 (c) and Fgure 3 (f). The scheme lmts the copes of content and a larger S consstently leads to smaller cost.

9 D. Effect of Zpf Parameter Fgure 4 studes the effect of the Zpf parameter α. By varyngαfrom. to 1.2, we can fnd that a largerαhelps acheve hgher delvery rato, lower average delay and cost for the scheme. For example, n Fgure 4 (a), the delvery rato of the scheme ncreases from 26.8% to 49.2% wth around 183% growth, and the average cost decreases from to wth around 31% reducton. These results are consstent wth our analyss n Secton IV, whch favors the skewed dstrbuton of p and q. In addton, for the MIT realty trace, Fgures 4 (d-f) ndcate the smlar growth of the delvery rato, and the reducton of the average delay and cost. For the Epdemc scheme, Fgures 4 (a) and (d) ndcate that the skewed dstrbuton has low effect on the delvery rato. It s because the Epdemc scheme blndly broadcasts content tems towards encounterng nodes and does not reduce the overall delvery rato. However, due to the default correlated dstrbuton of p and q, the Epdemc scheme ensures that an content tem easer encounters the needed nodes. Thus, the average delay and cost are reduced wth a larger α. Smlar stuaton occurs for the ProPHET and Bubble Rap approaches, though the reducton trend of average cost and delay s relatvely low compared wth the Epdemc scheme. E. Comparson of Three Schemes Fnally, we compare the scheme wth the broadcast and uncast schemes gven n Secton VI-A. Fgures 5 (a-c) plot the results of the Infocom6 trace. It s observed that ant-correlated topcs lead to less delvery rato and larger average delay and cost than correlated topcs. For example, for the scheme, the average cost wth antcorrelated topcs s decreased by 35.66%. Ths s because, f a topc s popular among moble devces, the developed optmzaton polcy proactvely relay the advertsements of such topcs wth a larger number of opportunstc encounters. Then, such opportunstc encounters beneft a larger number of content tems (due to the correlated topcs). It obvously leads to a hgher delvery rato and less average delay and cost. Among the three schemes, the scheme acheves the least average cost and comparable delvery rato and average delay as the broadcast scheme. It s because the scheme combnes the befts of both uncast and broadcast schemes. In addton, the uncast and broadcast schemes n ths fgure use less delvery rato than the ProPHET and Epdemc schemes, respectvely. It s because the optmal encounters gven by the developed optmzaton strategy can mprove the delvery of the popular advertsements, whch are hghly demanded by the majorty of moble devces. For the MIT realty data set, Fgures 5 (d-f) show the smlar trend as Fgures 5 (a-c). The scheme uses the least cost to acheve the comparable delvery rato. VIII. Concluson To tmely delver content over a DT, carefully adjusts the number of encounters and content copes for advertsed content, computes the utltes wth low mantenance cost to capture nterests and moblty patterns of moble devces, and develops a dstrbuted relay algorthm to select the best nodes as the carrers. Our experments demonstrate that the proposed scheme s able to acheve hgh delvery rato and sgnfcantly low overhead. Acknowledgment: Ths work s partally supported by Academy of Fnland (Grant o ), and we would lke to thank the anonymous SECO 12 revewers for ther valuable comments. Part of the research was also conducted n the Internet of Thngs program of Tvt (Fnnsh Strategc Centre for Scence, Technology and Innovaton n the feld of ICT), funded by Tekes. References [1] C. Boldrn, M. Cont, and A. Passarella. Modellng data dssemnaton n opportunstc networks. In Proceedngs of the thrd ACM workshop on Challenged networks, CHATS 8, ew York, Y, USA, 8. ACM. [2] L. Breslau, P. Cao, L. 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