Making Name-Based Content Routing More Efficient than Link-State Routing

Transcription

1 Makng Name-Based Content Routng More Effcent than Lnk-State Routng Ehsan Hemmat and J.J. Garca-Luna-Aceves, Comuter Engneerng Deartment, UC Santa Cruz, Santa Cruz, CA PARC, Palo Alto, CA { ehsan, jj }@soe.ucsc.edu arxv: v1 [cs.ni] 8 Ar 2018 Abstract The Dffusve Name-based Routng Protocol () s ntroduced for effcent name-based routng n nformatoncentrc networks (ICN). establshes and mantans multle loo-free routes to the nearest nstances of a name refx usng only dstance nformaton. elmnates the need for erodc udates, mantanng toology nformaton, storng comlete aths to content relcas, or knowng about all the stes storng relcas of named content. s sutable for large ICNs wth large numbers of refxes stored at multle stes. It s shown that rovdes loo-free routes to content ndeendently of the state of the toology, and that t converges wthn a fnte tme to correct routes to name refxes after arbtrary changes n the network toology or the lacement of refx nstances. The result of smulaton exerments llustrate that s more effcent than lnk-state routng aroaches. I. INTRODUCTION Several Informaton-Centrc Networkng (ICN) archtectures have been ntroduced to address the ncreasng demand of user-generated content [1], [3]. The goal of these archtectures s to rovde a cost-effcent, scalable, and moble access to content and servces by adotng a content-based model of communcaton. ICN archtectures seek to dssocate content and servces from ther roducers n such a way that the content can be retreved ndeendently of ts orgnal locaton or the locaton of consumers. The most romnent ICN archtectures can be characterzed as Interest-based archtectures, n whch locaton-ndeendent, self-defned, unque namng s used to retreve data. In ths aroach, messages flow from roducers to consumers based on the name of the content rather than the address of the senders or recevers exchangng such content. Content rovders or roducers create named data objects (NDOs), and advertse routable name refxes assocated wth the content objects whose own names are art of the name refxes. The only dentfer of an NDO s ts name. A consumer requests a ece of content by sendng an Interest (a request for the NDO) that s routed along content routers toward the roducer(s). Clearly, an effcent name-based content routng rotocol must be used for any ICN archtecture to succeed usng namebased forwardng of Interests and requested content. Secton II summarzes recent ror work n name-based content routng, and ths revew reveals that all ror roosals for name-based content routng rely on erodc transmssons of udate messages. Ths aer focuses on an aroach that avods the need c IFIP, 2018 Ths s the author s verson of the work. It s osted here by ermsson of IFIP for your ersonal use. Not for redstrbuton. ISBN , (2018) for erodc messagng by means of dffusng comutatons [5]. Secton III resents (Dffusve Name-based Routng Protocol), a name-based content routng rotocol for ICNs. rovdes multle loo-free routes to the nearest nstances of a named refx or to all nstances of a named refx usng only dstance nformaton and wthout requrng erodc udates, knowledge of the network toology, or the exchange of ath nformaton. Secton IV shows that revents routng-table loos even n the resence of toology changes as well as changes n the hostng of refxes, and converges wthn a fnte tme to correct mult-aths to name refxes. Secton V resents the results of smulaton exerments comarng wth an effcent lnk-state aroach smlar to NR [13]. The results show that roduces less communcaton and comutaton overhead n the case of toology changes as well as the addton of refxes. II. RELATED WORK Name-based content routng has been used n the ast n content-delvery networks (CDN) oeratng as overlay networks runnng on to of the Internet routng nfrastructure (e.g., [7], [16]). However, t has become more well known n the context of ICN archtectures, where t has been done tycally by adatng tradtonal routng algorthms desgned for networks n whch a destnaton has a sngle nstance [8]. Dstrbuted Hash Tables (DHT) are used n several archtectures as the name resoluton tool [11], [15], [18]. MobltyFrst [14] rely on an external and fast name resoluton system called Global Name Resoluton Servce (GNRS) that mas the data object names to network addresses. Some ICN archtectures use name resoluton mechansms to ma the name of the content to the content rovder. Data Orented Network Archtecture (DONA) [12] relaces DNS names wth flat, self-certfyng names and uses name resoluton to ma those flat names to corresondng IP addresses. DONA suorts host moblty and multhomng, and mroves servce access and data retreval. The Named-data Lnk State Routng rotocol (NR) [13] uses lnk state routng to rank the neghbors of a router for each name refx. Adjacency A and Prefx A, roagate toology and ublsher nformaton n the network resectvely. Each router uses toology nformaton and runs

2 an extenson of Djkstra s shortest-ath frst (SPF) algorthm to rank next hos for each router, then mas the refx to the name of the ublsher and creates routng table for each name refx. Lke most ror routng aroaches based on comlete or artal toology nformaton (e.g., [2], [6], [17]), NR uses sequence numbers to allow routers to determne whether the udates they receve have more recent nformaton than the data they currently store. As a consequence, these aroaches requre the use of erodc udates to ercolate throughout the network to ensure that all routers converge to consstent toology nformaton wthn a fnte tme. The Dstance-based Content Routng (DCR) [10] was the frst name-based content routng aroach for ICNs based on dstances to named content. DCR does not requre any nformaton about the network toology or knowledge about all the nstances of the same content. It enables routng to the nearest router announcng content from a name refx beng stored locally (called anchor), all anchors of a name refx, and subsets of anchors. Ths s attaned by means of multnstantated destnaton sannng trees (MIDST). Furthermore, DCR rovdes loo-free routes to reach any ece of named content even f dfferent content objects n the same refx are stored at dfferent stes. The lmtaton of DCR s that t requres erodc udates to be dssemnated through the network. III. fnds the shortest ath(s) to the nearest relca(s) of name refxes. To ensure that loo-free routes to named refxes are mantaned at every nstant ndeendently of the state of the network or refxes, establshes a lexcograhc orderng among the routes to refxes reorted and mantaned by routers. The lexcograhc orderng of routes s based on two suffcent condtons for loo freedom wth resect to a gven refx that allow for multle next hos to refxes along loo-free routes. dffuses the comutaton of new loofree routes when the loo-free condtons are not satsfed. The aroach used n s an extraolaton to the use of dffusng comutatons n [5]. Every ece of data n the network s a Named-Data Object (NDO), reresented by a name that belongs to a name refx or smly a refx advertsed by one or more roducer(s). Name refxes can be smle and human-readable or more comlcated and self certfyng, or may even be a crytograhc hash of the content. Content names can be flat or herarchcal. The namng schema deends on the system that runs and t s out of scoe of ths aer. A router attached to a roducer of content that advertses a name refx s called an anchor of that refx. At each router, calculates routes to the nearest anchor(s) of known name refxes, f there s any, and selects a subset of the neghbors of the router as vald next hos to reach name refxes, such that no routng-table loo s created at any router for any name refx. Cachng stes are not consdered content roducers and hence routes to cached content are not advertsed n. Our descrton assumes that routers rocess, store, and transfer nformaton correctly and that they rocess routng messages one at a tme wthn a fnte tme. Every router has a unque dentfer or a name that can be flat or herarchcal. The namng schema and name assgnment mechansm s out of scoe of ths aer. A. Messages and Data Structures Each router stores the lst of all actve neghbor routers (N ), and the cost of the lnk from the router to each such neghbor. The cost of the lnk from router to ts neghbor n s denoted by ln. Lnk costs can vary n tme but are always ostve. The lnk cost assgnment and metrc determnaton mechansms are beyond the scoe of ths aer. The routng nformaton reorted by each of the neghbors of router s stored n ts neghbor table (NT ). The entry of NT regardng neghbor n for refx s denoted by NTn and conssts of the name refx (), the dstance to refx reorted by neghbor n (d n), and the anchor of that refx reorted by neghbor n (a n). If router s the anchor of refx tself, then d = 0. Router stores routng nformaton for each known refx n ts routng table (RT ). The entry n RT for refx (RT) secfes: the name of the refx (); the dstance to the nearest nstance of that refx (d ); the feasble dstance to the refx (fd ); the neghbor that offers the shortest dstance to the refx (s ), whch we call the successor of the refx; the closest anchor to the refx (a ); the state mode (mf) regardng refx, whch can be PASSIVE or ACTIVE; the orgn state (o ) ndcatng whether router or a neghbor s the orgn of query n whch the router s actve; the udate flag lst (F L ); and the lst of all vald next hos (V ). F L conssts of four flags for each neghbor n. An udate flag (ufn) denotes whether or not the routng message should be sent to that neghbor. A tye flag (tfn) ndcates the tye of routng message the router has to send to neghbor n regardng refx (.e., whether t s an UPDATE, QUERY, or REPLY). A endng-rely flag (rfn) denotes whether the router has sent a QUERY to that neghbor and s watng for REPLY. A endng-query flag (qfn) s set f the router receved a QUERY from ts neghbor n and has not resonded to that QUERY yet. Router sends a routng message to each of ts neghbors contanng udates made to RT snce the tme t sent ts last udate message. A routng message from router to neghbor n conssts of one or more udates, each of whch carres nformaton regardng one refx that needs udatng. The udate nformaton for refx s denoted by U and states: (a) the name of the refx (); (b) the message tye (ut ) that ndcates f the message s an UPDATE, QUERY, or REPLY; (c) the dstance to ; and (d) the name of the closest anchor. The routng udate receved by router from neghbor n s denoted by Un. The udate nformaton of Un for refx, u n, secfes the refx name (), the dstance from n to that refx (ud n), the name of the anchor of that refx (ua n), and a message tye (ut n).

3 B. Suffcent Condtons for Loo Freedom The condtons for loo-free routng n are based on the feasble dstance mantaned at each router and the dstances reorted by ts neghbors for a name refx. One condton s used to determne the new shortest dstance through a loo-free ath to a name refx. The other s used to select a subset of neghbors as next hos to a name refx. Source Router Condton (SRC): Router can select neghbor n N as a new successor s for refx f: ( d n < ) ( d n < fd [d n = fd n < ] ) ( d n + l n = Mn{d v + l v v N } ). SRC smly states that router can select neghbor n as ts successor to refx f n reorts a fnte dstance to that refx, offers the smallest dstance to refx among all neghbors, and ether ts dstance to refx s less than the feasble dstance of router or ts dstance s equal to the feasble dstance of but n <. If two or more neghbors satsfy SRC, the neghbor that satsfes SRC and has the smallest dentfer s selected. If none of the neghbors satsfes SRC the router kees the current successor, f t has any. The dstance of router to refx, d, s defned by the dstance of the ath through the selected successor. A router that has a fnte feasble dstance (fd < ) selects a subset of neghbors as vald next hos at tme t f they have a fnte dstance to destnaton and are closer to destnaton. The followng condton s used for ths urose. Next-ho Selecton Condton (NSC): Router wth fd < adds neghbor n N to the set of vald next hos f: ( d n < ) ( d n < fd [d n = fd n < ] ). NSC states that router can select neghbor n as a next ho to refx f ether the dstance from n to refx s smaller than the feasble dstance of or ts dstance s equal to the feasble dstance and n <. NSC orders next hos lexcograhcally based on ther dstance to a refx and ther names. It s shown that no routng-table loos can be formed f NSC s used to select the next hos to refxes at each router. Note that the successor s also a vald next ho. The successor to a refx s a vald next ho that offers the smallest cost. SRC and NSC are suffcent condtons that, as we show subsequently, ensure loo-freedom at every nstance but do not guarantee shortest aths to destnatons. ntegrates these suffcent condtons wth nter-nodal synchronzaton sgnalng to acheve both loo freedom at every nstant and shortest aths for each destnaton. C. Oeraton A change n the network, such as a lnk-cost change, the addton or falure of a lnk, the addton or falure of a router, the addton or deleton of a refx, or the addton or deleton of a relca of a refx can cause one or more comutatons at each router for one or more refxes. A comutaton can be ether a local comutaton or a dffusng comutaton. In a local comutaton a router udates ts successor, dstance, next hos, and feasble dstance ndeendently of other routers n the network. On the other hand, n a dffusng comutaton a router orgnatng the comutaton must coordnate wth other routers before makng any changes n ts routng-table entry for a gven refx. allows a router to artcate n at most one dffusng comutaton er refx at any gven tme. A router can be n PASSIVE or ACTIVE mode wth resect to a gven refx ndeendently of other refxes. A router s PASSIVE wth resect to refx f t s not engaged n any dffusng comutaton regardng that refx. A router ntalzes tself n PASSIVE mode and wth a zero dstance to all the refxes for whch the router tself serves as an anchor. An nfnte dstance s assumed to any non-local (and hence unknown) name refx. Intally, no router s engaged n a dffusng comutaton (o = 0). When a PASSIVE router detects a change n a lnk or receves a QUERY or UPDATE from ts neghbor that does not affect the current successor or can fnd a feasble successor, t remans n PASSIVE mode. On the other hand, f the router cannot fnd a feasble successor then t enters the ACTIVE mode and kees the current successor, udates ts dstance, and sends QUERY to all ts neghbors. Table I shows the transt from one state to another. Neghbor k s a neghbor other than the successor s. Mode State Event Passve 0 Actve TABLE I STATE TRANSIT IN Events from a neghbor k, SRC satsfed 0 Events from a neghbor k, SRC not satsfed 1 QUERY from the Successor 3 Receves last REPLY 0 Change n dstance to Successor 2 QUERY from the Successor 4 Receves last REPLY, SRC satsfed 0 Receves last REPLY, SRC not satsfed 1 QUERY from the Successor 4 Receves last REPLY 0 Change n dstance to the Successor 4 Receves last REPLY, SRC satsfed 0 Receves last REPLY, SRC not satsfed 3 Next State Algorthm 1 shows the rocessng of messages by a router n PASSIVE mode. Algorthm 2 shows the stes taken n ACTIVE mode. Algorthm 3 shows the stes taken to rocess a routng udate. Handlng A Sngle Dffusng Comutaton: Routers are ntalzed n PASSIVE mode. Each router contnuously montors ts lnks and rocesses the routng messages receved from ts neghbors. When router detects a change n the cost or state of a lnk, or a change n ts neghbor table that causes a change n ts dstance to refx (d ), t frst tres to select a new successor that satsfes SRC. If such a successor exsts, the router carres out a local comutaton, udates ts dstance, successor, and closest anchor, and exts the comutaton. In a local comutaton, router comutes the mnmum cost to reach the destnaton and udates d = mn{d n + l n n

4 N }. If ts dstance changes, router sends a routng message wth ut = UPDATE. Router also udates ts feasble dstance to equal the smaller of ts value and the new dstance value,.e., fd (new) = mn{fd (old), d }. An UPDATE message from a neghbor s rocessed usng the same aroach stated above. If a router receves a QUERY from ts neghbor other than ts successor whle t s n PASSIVE mode, t udates the neghbor table, checks for a feasble successor accordng to SRC and reles wth d, f t succeeds. If router cannot fnd a neghbor that satsfes SRC after a change n a lnk or neghbor-table entry, then t starts out a dffusng comutaton by settng the new dstance as the dstance through ts current successor, enters the ACTIVE mode (mfj = ACTIVE) and sets the corresondng flag (rf n) for each neghbor n. After enterng the ACTIVE mode, router sets the new dstance as the cost of the ath through the current successor (d = d s + l s and sends a routng message ) wth ut = QUERY. Router uses the endng rely flag (rfn) to kee track of the neghbors from whch a REPLY has not been receved. When a router becomes ACTIVE t sets the udate flag (uf = 1), and also sets the tye flags (tf = QUERY n N ) and sends the routng messages to all ts neghbors. Algorthm 1 Processng routng messages n PASSIVE mode INPUT: RT, NT, ln, u n; [o] verfy u n; d n = ud n; d mn = ; for each k N {} do f (d k +lk < d mn) (d k +lk = d mn k < s new ) then s new = k; d mn = d k + lk; f (d s new < fd [d s new = fd s new < ]) then f s s new then s = s new; a = a s new f d d mn then d = d mn; fd = mn{fd, d }; V = φ; for each k N {} do ufk = 1; tfk =UPDATE; f (d k < fd [d k = fd k < ]) then V = V k; f ut n = QUERY then tf =REPLY; else mf = ACTIVE; d = d s + l s ; f (n = s ut n = QUERY) then o = 3; else o = 1; for each k N {} do uf = 1; tf =QUERY; When a router s n ACTIVE mode, t cannot change ts successor or fd untl t receves the reles to ts QUERY from all ts neghbors. After recevng all reles (.e. rf n = 0 n N ), router becomes PASSIVE by resettng ts feasble dstance. The router then selects the new successor and sends UPDATE messages to ts neghbors. More secfcally, router sets fd = whch nsures that the router can fnd a new successor that satsfes SRC and then sets fd = d = mn{d n + l n n N } and becomes PASSIVE. Algorthm 2 Processng routng messages n ACTIVE mode INPUT: RT, NT, u n; [o] verfy u n; d n = ud n; f ut n = REPLY then rf n = 0; lastrely = true; for each k N {} do f rf k = 0 then lastrely = false; f lastrely = true then f o = 1 o = 3 then fd = Execute Algorthm 3 else f ut n = QUERY then f (o = 1 o = 2) then f n s then uf n = 1; tf n =REPLY; else o = 4; f (o = 3 o = 4) then uf n = 1; tf n =REPLY; Algorthm 3 Udate RT INPUT: RT, NT, ln, u n; d mn = ; for each k N {} do f (d k +lk < d mn) (d k +lk = d mn k < s new ) then s new = k; d mn = d k + lk; f (d s new < fd [d s new = fd s new < ]) then o = 0; mf = P ASSIV E; f s s new then s = s new; f d d mn then d = d mn; fd = mn{fd, d }; V = φ; for each k N {} do ufk = 1; tfk =UPDATE; f (d k < fd [d k = fd k < ]) then V = V k; f qf s (old) = 1 then tf =REPLY; else f o = 2 then o = 1 else o = 3; for each k N {} do uf = 1; tf =QUERY; If router receves a QUERY from a neghbor other than ts successor whle t s ACTIVE, t smly reles to ts neghbor wth a REPLY message statng the current dstance to the destnaton. The case of a router recevng a QUERY from ts successor whle t s ACTIVE s descrbed subsequently n the context of multle dffusng comutatons. UPDATE messages are rocessed and neghbor tables are udated, but the successor or dstance s not changed untl the router receves all the reles t needs to transton to the PASSIVE mode. Whle a router s n ACTIVE mode, nether a QUERY nor an UPDATE can be sent.

5 Fg. 1. Oeraton Examle Handlng Multle Dffusng Comutatons: Gven that a router executes each local comutaton to comleton, t handles multle local comutatons for the same refx one at a tme. Smlarly, a router handles multle dffusng comutaton for the same refx by rocessng one comutaton at a tme. An ACTIVE router can be n one of the followng four states: (1) router orgnated a dffusng comutaton (o = 1), (2) metrc ncrease detected durng ACTIVE mode (o = 2), (3) dffusng comutaton s relayed (o = 3), or (4) successor metrc changed durng ACTIVE mode (o = 4). If the router s n PASSIVE mode then ts state s 0 (.e., o = 0). Consder the case that a router s ACTIVE and n State 1 (o = 1). If the router receves the last REPLY to ts query, then t resets ts feasble dstance to nfnty, checks SRC to fnd the new successor, and sends an UPDATE to all ts neghbors. On the other hand, f router detects a change n the lnk to ts successor then t udates ts neghbor table and sets o = 2. If router s n State 2, receves the last REPLY, and can fnd a feasble successor usng SRC wth the current feasble dstance, then t becomes PASSIVE and sends an UPDATE to all ts neghbors(o = 0). Otherwse, t sends a QUERY wth the current dstance and sets o = 1. Router uses the endng query flag (qf n) to kee track of the reles that have been receved for ts QUERY regardng refx. If router s n ether State 1 or 2 and receves a QUERY from ts current successor to the refx, then t sets qf s =1 and transtons to State 4 (.e., t sets o = 4). If a router n PASSIVE mode receves a QUERY from ts successor, t searches for a new successor that satsfes SRC. If t cannot fnd such a successor then t kees the current successor, udates ts dstance, and becomes ACTIVE. Then, the router sends QUERY to all of ts neghbors and sets o = 3. When router n state 3 receves REPLY from all of ts neghbors, t resets ts feasble dstance, fd =, selects a new successor, udates the V and sends UPDATE to ts neghbors and REPLY to ts the revous successor. If the router detects a lnk falure or a cost ncrease n the lnk to ts current successor, the router sets o = 4 to ndcate that a toology change occurred whle the router s n ACTIVE mode. A router handles the case of the falure of the lnk wth ts successor as f t had receved a REPLY from ts successor wth d s =. If router s n State 4, (o = 4) and t receves reles from all ts neghbors, then t tres to fnd a feasble successor that satsfes SRC wth the current value of fd. If such a successor exsts, the router udates ts successor, dstance, and next hos for refx, and sends an UPDATE message to ts neghbors as well as REPLY to the revous successor. Otherwse, t sets o = 3 and sends a QUERY wth the new dstance. Whle router s n ACTIVE mode regardng a refx, f a QUERY s receved for the refx from a neghbor other than the current successor, the router udates the neghbor table and sends a REPLY to that neghbor. If a router n PASSIVE mode receves a QUERY from a neghbor other than the current successor, the router udates ts neghbor table. If the feasblty condton s not satsfed anymore, the router sends a REPLY to the neghbor that rovdes the current value d before t starts ts own comutaton. D. Examle of Oeraton Fgure 1 llustrates the oeraton of wth a smle examle. The fgure shows the routng nformaton used for a sngle refx when routers a and z advertse that refx and each lnk has unt cost. The tule next to each router states the dstance and the feasble dstance of the router for that refx. The red, blue, and green arrows reresent the QUERY, REPLY, and UPDATE messages resectvely and the number next to the arrow shows the tme sequence n whch that message s sent. Fgure 1 (a) shows the change n the cost of lnk (r, a). Router r detects ths change and becomes ACTIVE and sends QUERY to ts neghbors. Router q receves the QUERY from ts successor and cannot fnd a feasble successor (Fgure 1(b)). Therefore, t becomes ACTIVE and sends a QUERY to ts neghbors. Router r receves REPLY from a and t, and a QUERY from q. Gven that q s not a successor for router r, r sends REPLY to q. After recevng REPLY from routers r, s and t, router q becomes PASSIVE agan and sends ts REPLY to ts revous successor, r. In turn, ths means that r receves all the reles t needs, becomes PASSIVE, and resets ts feasble dstance. The oeraton of s such that only a orton of the routers are affected by the toology change.

6 E. Routng to all nstances of a refx enables routers to mantan multle loo-free routes to the nearest anchor of a name refx. In some ICN archtectures, such as NDN and CCNx, an anchor of a namerefx may have some but not necessarly all the content corresondng to a gven refx. Therefore, smly routng to nearest relca may cause some data to be unreachable, and the ablty to contact all anchors of a refx s needed. To address ths case, a mult-nstantated destnaton sannng tree (MIDST) can be used alongsde to suort routng to all anchors of the same refx. A MIDST s establshed n a dstrbuted manner. Routers that are aware of multle anchors for the same refx exchange routng udates to establsh the sannng tree between all anchors of a refx. Once the MIDST s formed for a gven refx, the frst router n the MIDST that receves a acket forwards t over the MIDST to all of the anchors. The detals of how a MIDST can be establshed n are omtted for brevty; however, the aroach s very much the same as that descrbed n [9]. IV. CORRECTNESS OF The followng theorems rove that s loo-free at every nstant and consders each comutaton ndvdually and n the roer sequence. From these results, the roof that converges to shortest aths to refxes s smlar to the roof resented n [4] and due to sace lmtaton s omtted. We assume that each router receves and rocesses all routng messages correctly. Ths mles that each router rocesses messages from each of ts neghbors n the correct order. Theorem 1: No routng-table loos can form n a network n whch routers use NSC to select ther next hos to refxes. Proof: Assume for the sake of contradcton that all routng tables are loo-free before tme t l but a routng-table loo s formed for refx at tme t l when router q adds ts neghbor n 1 to ts vald next-ho set V q. Because the successor s also a vald next ho, router q must ether choose a new successor or add a new neghbor other than ts current successor to ts vald next-ho set at tme t l. We must show that the exstence of a routng-table loo s a contradcton n ether case. Let L be the routng-table loo consstng of h hos startng at router q, (L = {q = n 0,new, n 1,new, n 2,new,..., n h,new }) where n h,new = q, n +1,new V n for 0 h. The tme router n udates ts vald next-ho set to nclude n +1,new s denoted by t new. Assume that the last tme router n sent an UPDATE that was rocessed by ts neghbor n 1, s t old. Router n revsts vald next hos after any changes n ts successor, dstance, or feasble dstance; therefore, t old t new t l and d n (t l ) = d n (t old ). Also, by defnton, at any tme t, fd (t ) d (t ), and fd (t 2 ) fd (t 1 ) f t 1 < t 2. Therefore, fd (t 2 ) d (t 1 ) such that t 1 < t 2 (1) If router n selects a new successor at tme t new then: d n 1 (t l ) = d n (t old ) fd n (t old ) fd n (t new ) (2) Usng NSC ensures that (fd n (t new ) > d n (t l )) (fd n (t new ) = d n (t l ) n > n +1 ) From Eqs. (2) and (3) we have: (d n 1 (t l ) > d n (t l )) (d n 1 (t l ) = d n (t l ) n > n +1 ) Therefore, for 0 k h n L t s true that: (d n0 n 1 (t l ) > d n k n k+1 (t l )) (d n0 n 1 (t l ) = d n k n k+1 (t l ) n 0 > n k ) If d n 1 (t l ) > d n (t l ) n at least one ho n L then t must be true that, for any gven k {1, 2,..., h}, d n k n k+1 (t l ) > d n k n k+1 (t l ), whch s a contradcton. If at any ho n the L t s true that d n 1 (t l ) = d n (t l ), then k > k, whch s also a contradcton. Therefore, no routngtable loo can be formed when routers use NSC to select ther next hos to refx. Lemma 2: A router that s not the orgn of a dffusng comutaton sends a REPLY to ts successor when t becomes PASSIVE. Proof: A router that runs can be n ether PASSIVE or ACTIVE mode for a refx when t receves a QUERY from ts successor regardng the refx. Assume that router s n PASSIVE mode when t receves a QUERY from ts successor. If router fnds a neghbor that satsfes SRC, then t sets ts new successor and sends a REPLY to ts old successor. Otherwse, t becomes ACTIVE, sets o = 3, and sends a QUERY to all ts neghbors. Router cannot receve a subsequent QUERY from ts successor regardng the same refx, untl t sends a REPLY back to ts successor. If the dstance does not ncrease whle router s ACTIVE then o remans the same (.e. o = 3). Otherwse, router must set o = 4. In both cases router must send a REPLY when t becomes PASSIVE. Assume that router s n ACTIVE mode when t receves a QUERY from ts successor s. Router s cannot send another QUERY untl t receves a REPLY from all ts neghbors to ts query, ncludng router. Hence, router must be the orgn of the dffusng comutaton for whch t s ACTIVE when t receves the QUERY from s, whch means that o = 1 or o = 2. In both cases router sets o = 4 when t receves a QUERY form ts successor s and s must send a REPLY n resonse to the QUERY from because, s not the successor for s. After recevng the last REPLY from ts neghbors, ether router fnds a feasble successor and sends a REPLY to s (o = 0) or t roagates the dffusng comutaton forwarded by s by sendng a QUERY to ts neghbors and settng o = 3. Router then must send a REPLY to s when t receves the last REPLY for the QUERY t forwarded from s. (3) (4) (5)

7 Hence, ndeendently of ts current mode, router must send a REPLY to a QUERY t receves from ts successor when t becomes PASSIVE. Lemma 3: Consder a network that s loo free before an arbtrary tme t and n whch a sngle dffusng comutaton takes lace. If node n s PASSIVE for refx at that tme, then t must be true that (dn n 1 (t) > d n (t)) (d n 1 (t) = d n (t) n > n +1 ) ndeendently of the state of other routers n the chan of vald next hos {n 1, n, n +1 } for refx. Proof: Assume that router n s PASSIVE and selects router n +1 as a vald next ho. Accordng to NSC t must be true that: (d n (t) < fd n (t) d n (t)) (d n (t) = fd n (t) d n (t) n +1 < n ) Assume that n dd not reset fd n the last tme t new < t when n became PASSIVE and selected ts successor s new and udated ts dstance d n (t new ) = d n (t). If router n 1 rocessed the message that router n sent after udatng ts dstance, then: dn n 1 (t) = d n (t new ). Substtutng ths equaton n 6 renders the result of ths lemma. On the other hand, If router n 1 dd not rocess the message that router n sent after udatng ts dstance and before t, then d n 1 (t) = d n (t old ). Based on the facts that router n dd not reset ts feasble dstance and Eq. 1 holds for ths case. Therefore: d n 1 (6) (t) = d n 1 (t old ) > fd n (t) (7) Now consder the case that n becomes PASSIVE at tme t new and changes ts successor from s old to s new by resetng ts feasble dstance. The case that n 1 rocessed the message that router n sent after becomng PASSIVE s the same as before. Assume that n 1 dd not rocess the message that n sent at tme t new. Furthermore, assume that router n becomes ACTIVE at tme t old, wth a dstance d n (t old ) = d n s old + ls n old. Router n cannot change ts successor or exerence any ncrement n ts dstance through s old ; hence, d n (t new ) d n (t old ). On the other hand, the dstance through the new successor must be the shortest and so d n (t new ) = d n s new + d n (t old ). Router n becomes PASSIVE f t receves a l n s new REPLY from each of ts neghbors ncludng n 1. Therefore, n 1 must be notfed about d n (t old ). Therefore: d n 1 (t) = d n (t old ) d n (t new ) = d n (t). (8) Substtutng ths equaton n 6 renders the result of ths lemma. Therefore, the lemma s true n all cases. Lemma 4: Consder a network that s loo free before an arbtrary tme t and n whch a sngle dffusng comutaton takes lace. Let two network nodes n and n +1 be such that n +1 V n. Indeendently of the state of these two nodes, t must be true that: (fd n (t) > fd n+1 (t)) (fd n (t) = fd n+1 (t) n > n +1 ) (9) Proof: Consder the case that router n s PASSIVE, then from Lemma 3 and the fact that routers select ther next hos based on NSC, t must be true that: (fd n (fd n > d n (t)) = d n (t) n > n +1 ) (10) Consder the case that router n +1 s ACTIVE. Router n +1 cannot change ts successor or ncrease ts feasble dstance. If router n rocessed the last message that router n +1 sent before tme t, then: d n (t) = fd n+1 (t) and the lemma s true. Assume router n dd not rocess the last message that router n +1 sent before tme t. Router n must send a REPLY to n +1 the last tme that router n +1 became PASSIVE at tme t reortng a dstance d n+1 (t old ) = d n+1 s old + ls n+1 old. If router n +1 dd not reset ts feasble dstance snce the last tme t became assve, fd n+1, then, d n+1 (t old ) fd n+1 (t). Consder the case that router n +1 resets fd n+1 the last tme before t that t becomes PASSIVE. Router n +1 cannot change ts successor or exerence any ncrement n ts dstance through ts old successor, s old. Hence, d n+1 (t new ) (t old ). On the other hand, the dstance through the new d n+1 successor must be the smallest among all neghbors ncludng the old successor and so d n+1 (t new ) = (d n+1 s new + ls n+1 new ) d n+1 (t old ). Router n +1 becomes PASSIVE f t receves a REPLY from each of ts neghbors, ncludng n. Therefore, n must be notfed about d n+1 (t old ). Therefore, d n (t) = d n+1 (t old ) d n+1 (t new ) fd n+1 (t new ) (11) The feasble dstance fd n+1 (t new ) wth t new < t cannot ncrease untl router n +1 becomes PASSIVE agan; therefore,fd n+1 (t new ) fd n (t). The result of the lemma follows n ths case by substtutng ths result n Eqs. (11) and Eq. (10). Now consder the case that router n +1 s PASSIVE. If router n rocessed the last message that router n +1 sent before tme t, then d n (t) = d n+1 (t) fd n+1 (t) and the lemma s true. Now consder the case that router n dd not rocess the last message router n +1 sent before tme t. If router n +1 dd not reset fd n+1 then d n+1 (t old ) fd n+1 (t). On the other hand, f router n +1 resets fd n+1 then we can conclude that fd n+1 (t new ) fd n (t) and n > n +1 usng an argument smlar to one we used for the ACTIVE mode. Hence, the lemma s true for all cases. NSC and SRC guarantees loo-freedom at every tme nstant. If we consder the lnk form router to ts vald next ho wth resect to a secfc refx as a drected edge, then the grah contanng all ths drected lnks s a drected acyclc grah (DAG) wth resect to that secfc refx. The DAG reresentng the relatonsh of vald next hos regardng refx s denoted by D. Lemma 5: If routers are nvolved n a sngle dffusng comutaton then D s loo-free at every nstant. Proof: Assume for the sake of contradcton that D s loo-free before an arbtrary tme t and a loo L consstng of h hos s created at tme t l > t when router q udates V q after

8 num. messages Add Prefx num. messages Delete Prefx num. messages Lnk Falure num. messages Lnk Recovery num. oeratons num. of relcas (a) Add Prefx num. oeratons num. of relcas (b) Delete Prefx num. oeratons num. of relcas (c) Lnk Falure num. oeratons num. of relcas (d) Lnk Recovery 10 0 num. of relcas (e) 10 0 num. of relcas (f) 10 0 num. of relcas (g) 10 0 num. of relcas (h) Fg. 2. Smulaton results showng average number of messages and average number of oeratons vs number of relcas rocessng an nut event. Assume that L = {n 1, n 2,..., n h } s the loo created, where n +1 V n for 1 h and n 1 V n h. If router n 1 changes ts next ho as a result of changng ts successor, t must be n PASSIVE mode at tme t l because an ACTIVE router cannot change ts successor or udate ts next-ho set. If all routers n L are PASSIVE at tme t l, ether all of them have always been PASSIVE at every nstant before t l, or at least one of them was ACTIVE for a whle and became PASSIVE before t l. If no router was ever ACTIVE before tme t l, t follows from Theorem 1 that udatng V n cannot create loo. Therefore, for router n 1 to create a loo, at least one of the routers must have been ACTIVE before tme t. If all routers are n PASSIVE mode at tme t, traversng L and alyng Theorem 10 leads to the erroneous concluson that ether d n1 > d n1 or n 1 > n 1. Therefore udatng V n1 cannot create a loo f all routers n the L are PASSIVE at tme t. Assume that only one dffusng comutaton s takng lace at tme t l. Based on Lemma 4 traversng loo L leads to the concluson that ether fd n > fd n or n > n, whch s a contradcton. Therefore, f only a sngle dffusng comutaton takes lace, then L cannot be formed when routers use SRC and NSC along wth dfusng comutatons to select next hos to reach the destnaton refx. At steady state, the grah contanng the successors and connected lnks between them, must create a tree. The tree contanng successors that are ACTIVE regardng refx and artcatng n a dffuson comutaton started form router at tme t are called dffusng tree (T (t)). Theorem 6: consders each comutaton ndvdually and n the roer sequence. Proof: Assume router s the only router that has started a dffusng comutaton u to tme t. If router generates a sngle dffuson comutaton, the roof s mmedate. Consder the case that router generates multle dffusng comutatons. Any router that s already artcatng n the current dffusng comutaton (routers n the T, ncludng the router ) cannot send a new QUERY untl t receves all the reles to the QUERY of the current comutaton and becomes PASSIVE. Note that each router rocesses each event n order. Also, when a router becomes PASSIVE, t must send a REPLY to ts successor, f t has any. Therefore, all the routers n T must rocess each dffusng comutaton ndvdually and n the roer sequence. Consder the case that multle sources of dffusng comutatons exst regardng refx n the network. Assume router s ACTIVE at tme t. Then ether router s the orgnator of the dffusng comutaton (o = 1 or 2), or receved a QUERY from ts successor (o = 3 or 4). If o = 1 or 3, the router must become PASSIVE before t can send another QUERY. If the router s the orgnator of the comutaton (o = 1 or 2) and receves a QUERY form ts successor, t holds that QUERY and sets o =4. Therefore, all the routers n the T reman n the same comutaton. Router can forward the new QUERY and become the art of the larger T s only after t receves a REPLY form each of ts neghbors for the current dffusng comutaton. If router a s ACTIVE and receves a QUERY from ts neghbor k s a, then t sends a REPLY to ts neghbor before creatng a dffusng comutaton, whch means that T a s not art of the ACTIVE T to whch k belongs. Therefore, any two ACTIVE T and T j have an emty ntersecton at any gven tme, t thus follows from the revous case that the Theorem s true. V. PERFORMANCE COMPARISON We comare wth a lnk-state routng rotocol gven that NR [13] s based on lnk states and s the routng rotocol advocated n NDN, one of the leadng ICN archtectures. We mlemented and an dealzed verson of NR, whch we smly call I (for deal lnk-state), n ns-3 usng the needed extensons to suort content-centrc networkng [19]. In the smulatons, I roagates udate messages usng the ntellgent floodng mechansm. There are two tyes of Lnk State Advertsements (A): An adjacency

9 A carres nformaton regardng a router, ts neghbors, and connected lnks; and a refx A advertses name refxes, as secfed n [13]. For convenence, sends HELLO messages between neghbors to detect changes n the sate of nodes and lnks. However, HELLO s can be omtted n a real mlementaton and detectng node adjacences can be done my montorng acket forwardng success n the data lane. The AT&T toology [20] s used because t s a realstc toology for smulatons that mmc art of the Internet toology. It has 154 nodes and 184 lnks. A node has 2.4 neghbors on average. In the smulatons, the cost of a lnk s set to one unt, and 30 nodes are selected as anchors that advertse 1200 unque name refxes. We generated test cases consstng of sngle lnk falure and recovery, and a sngle refx addton and deleton. To comare the comutaton and communcaton overhead of and I, we measured the number of routng messages transmtted over the network and the number of oeratons executed by each routng rotocol. The number of messages for I ncludes the number of HELLO messages, Adjacency As, and Prefx As. For, ths measurement ndcates the total number of all the routng messages transmtted as a result of any changes. The oeraton count s ncremented whenever an event occurs, and statements wthn a loo are executed. The smulaton results comarng wth I are dected n Fgure 2. In each grah, the horzontal axes s the average number of anchors er refx,.e., the number of anchors that advertse the same refx to the network. We consdered four scenaros: addng a new refx to the network; deletng one refx from one of the relcas; a sngle lnk falure; and a sngle lnk recovery. Hence, I ncurs the same sgnalng overhead ndeendently of how many A s are carred n an udate. Fgures (2a - 2d) showthe number of messages transmtted n the whole network whle Fgures (2e - 2h) show the number of oeratons each rotocol executed after the change. The number of oeratons n the fgure s n logarthmc scale. I advertses refxes from each of the relcas to the whole network. As the number of relcas ncreases, the number of messages ncreases, because each relca advertses ts own Prefx A. In, addng a new refx affects nodes n small regons and hence the number of messages and oeratons are fewer than n I. Deletng a refx from one of the relcas results n several dffusng comutatons n, whch results n more sgnalng. However, the number of messages decreases as the number of relcas ncreases, because the event affect fewer routers. In I one Prefx A wll be advertsed for each deleton. The comutaton of refx deleton s comarable; however, moses less comutaton overhead when the number of relcas reach 4. has less communcaton overhead comared to I after a lnk recovery or a lnk falure. The need to execute Djkstra s shortest-ath frst for each neghbor results n I requrng more comutatons than. outerforms NR for toology changes as well as addng a new refx. VI. CONCLUSION We ntroduced the frst name-based content routng rotocol based on dffusng comutatons () and roved that t rovdes loo-free mult-ath routes to mult-homed name refxes at every nstant. Routers that run do not requre to have knowledge about the network toology, use comlete aths to content relcas, know about all the stes storng relcas of named content, or use erodc udates. has better erformance comared to lnk-state routng rotocols when toology changes occur or new refxes are ntroduced to the network. A real mlementaton of would not requre the use of HELLO s used n our smulatons, and hence ts overhead s far less than routng rotocols that rely on A s valdated by sequence numbers, whch requre erodc udates to work correctly. VII. ACKNOWLEDGMENTS Ths work was suorted n art by the Baskn Char of Comuter Engneerng at UCSC. REFERENCES [1] M. Bar et al., A Survey of Namng and Routng n Informaton-Centrc Networks, IEEE Communcatons Magazne, vol. 50, no. 12, , Dec [2] J. Behrens and J.J. 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