Iteratoal Joural of Grd Dstrbuto Computg, pp.141-150 http://dx.do.org/10.14257/jgdc.2015.8.6.14 IP Network Topology Lk Predcto Based o Improved Local Iformato mlarty Algorthm Che Yu* 1, 2 ad Dua Zhem 1 1 Northwester Polytechcal Uversty, chool of Electrocs ad Iformato, hax X a, 710072 2 Zhegzhou Isttute of Aeroautcal Idustry Maagemet, Hea Zhegzhou, 450015 cheyu3440@gmal.com Abstract Wth the expaso of the IP etwork scale, the topology structure of IP etwork has also chagg. Tradtoal etwork topology research methods by adaptg tools of Pg or Traceroute were used to carry out the actve ed-to-ed detecto from the org router odes to destato router odes. But sometmes, because some routers set the UDP/NMP lmtato, there are some router IP address could ot be detected. I addto, A operator ca adopt router syslog cofgurato fles to obta lk coecto codto, but, these fles have the update lfe-tme, t s hard to obta the formato real-tme. o, we oly obtaed some complete topology formato. Due to the IP etwork has some local formato smlarty, ths artcle adopted the complex lk predcto algorthm based o local formato smlarty algorthm ad desg a kd of mproved method based o the IP etwork characters to realze the ukow lks predcto. Through the expermet, the results expressed that, the predcto dex of local formato commo eghbor algorthm dex of AA, RA obta the most good accuracy, ad the mproved Bayesa CN dex combg the degree value dex of AA ca get more hgher predcto accuracy about 0.97. Ths artcle cofrmed the lk predcto method based o local formato smlarty algorthm ca be effectvely appled the IP etwork ukow lk predcto. Keywords: IP etwork, topology structure, lk predcto, smlarty dex, local formato smlarty 1. Itroducto IP etwork s composed of multple autoomous area (A), each area usually use teral gateway protocol (IGP) of ICMP, NMP, RIP, OPF, etc. Amog them, usg NMP protocol to buld etwork topology s the more commo way. Through the operatg of the MIB database the maaged devces, operators ca extract the avalable formato to buld topology. [1] However, f the router coecto relato has chaged, Mb lbrary dd ot upgrade, the coecto relato s ot accurate. Wth the ad of hared Rsk Lk Groups (RLGs), operator ca real-tme obta curret IP coecto relatos, but aalyss s laborous. [2] I addto, by examg the router cofgurato fle ca also uderstad the router coecto wth other routers, but update exts lfetme, the formato s o completely accuracy. Based o ICMP protocol of Pg detecto tools to actvely detect router ode etwork, t eed to sed a lot of detecto data packet, whch s boud to crease etwork traffc, ad brg uecessary obstructo to local area etwork (LAN). 1 1 Che Yu s the correspodg author. IN: 2005-4262 IJGDC Copyrght c 2015 ERC
Iteratoal Joural of Grd Dstrbuto Computg O large IP etwork coecto test, because of usg the A BGP routg protocols for securty reasos, may routers set a lmt to ba the Pg jursdcto, operators uable to obta etwork topology formato. Ad because of the large amout of log data free text format, curret research scholars use router syslog to uderstad the coecto relato of each router s more dffcult to parse. [3] I ths paper, wth the ad of lk predcto algorthm, we explore the IP etwork structure, uder uderstadg part of the relatos of the router coecto, predct the IP etwork topology structure. I ths paper, chapter 2 troduces the IP etwork model buldg ad lk predcto bass, chapter 3 troduces lk predcto algorthm ad related dcators, chapter 4 presets the IP etwork topology predcto expermets by usg the AUC for accurate dagoss, ad descrbes the lk performace betwee the tradtoal algorthm ad the mproved predcto algorthm the IP etwork lk predcto, chapter 5 cocludes the paper ad put forward the further work. 2. IP Network Model Buld ad Predcto Bass 2.1. IP Network Model Each etwork ode o IP etwork ad the coecto relatos amog them cossts a u-drecto coected graph. Each vertex geerally refers to the etwork odes such as router, swtch, host, sub-et. The edge coectg each vertex expresses the lk betwee the equpmet. The ultmate goal of topology dscovery algorthm s as accurately as possble to fd the vertexes ad edges of the u-drecto coected graph. Fgure 1, respectvely presets a IP etwork cotag three A [4]. We use the umbers to detfy the tra-router or ter-doma router, etc, ad express the coecto relato by the dfferet thckess sold le. The order of ID umbers s defed by the router level from the border router to the er router from 1 to 11. Ad the H1 ad H2 s ed-to-ed detecto computer, we ca adopt them to realze the lk coecto state detecto whe the lks are good. 5 1 6 4 2 3 11 7 8 9 10 H1 H2 2.2. Topology Predcto Bass Fgure 1. IP Network Model Dagram Based o the structural feature of IP etwork, we use lk predcto method based o structure smlarty, uder obtaed some router coecto relato; we try to predct the etwork topology relato. To a large IP etwork, we buld a model of a powerless ad u-drecto coected etwork G (V, E). Amog them, V represets a collecto of odes, such as the routers, swtches; E s a collecto of lks. Assumes that a etwork the router ode umber s N, the total lk umber s M. I the etwork, t cossts of N (N - 1) / 2 odes. As show Fgure 1, there are 11 router odes, therefore, all of the odes should have 55 umbers of coecto lks, but ow oly 14 umbers of actual lk coecto. Ad fact, there may be some of lk coectos relatoshp does t 142 Copyrght c 2015 ERC
Iteratoal Joural of Grd Dstrbuto Computg be detected whe carryg out the actve ed-to-ed detecto. But a local A, the lk coecto has some smlarty character, so, we cosder a kd of lk predcto algorthm to predct the ukow lk coecto. I order to measure ad evaluate the effect of the lk predcto, amely order to test the accuracy of algorthm, we eed to dvde the ed-to-ed detects lk formato (amely kow lk E) radom to two parts of the trag set E T ad the testg set E P. The codto of trag lk set act as kow formato to use, whe calculatg the score value betwee the two router, we ca oly use the formato of ths set, ad the lk codto to the test set do t act as the kow formato to predct, but order to use them to evaluate the result of the predcto. Itutvely, there are the relatos betwee the set as Formula (1). T E E E, P E T P E (1) We ca see that the lk belogs to the complete set U, but ot belogs to E s exstet lk actual codto. Measurg the accuracy dex of the lk predcto method maly has three kds: respectvely cludes the area uder the recever operatg characterstc curve (AUC) dex, precso dex (PI) ad rakg score dex (RI). [5] Whe measurg the accuracy, the emphass focus s slghtly dfferet, AUC maly measure the accuracy of the algorthm from the overall, PI s a part dex, oly cosder the top umbers L of predct edge whether accurate or ot, RI s more atteto s to sort the predct edge. I ths artcle, we use the AUC dex to vald the accuracy of predctg lk. The AUC ca be defed as Formula (2). accurcy ( 1 0.5 2) / (2) We ca see, the value of AUC gets more tha 0.5, whch expresses how much degree the predcto value s superor to the radom selecto. For example, Fgure 1, there are 11 umbers of odes, 14 umbers of lks ca be detected, but the etwork total possbly has 55 umbers of lk coecto relatoshps, so, there are 41 umbers of lks are exstet coecto. I order to test the algorthm precso, we eed to select some umbers of lks from the kow lks of (1,5), (5,6), (1,6), (1,4), (3,4), (2,7), (7,8), (4,9), ad (9,10) as test set, ad the rest umbers of lks as trag test. If we select 6 trag lks, rest 3 umbers of lk ad 46 umbers of ukow lks, t should carry out 46*6=276 tmes of comparsos. Ad whe the score value of kow lk s bgger tha exstet lk, the value of AUC add 1, f the score value of test lk s equal to exstet lk, the value of AUC add 0.5, f the score value of exstet lk s bgger tha test lk, the value of AUC add zero. 3. Lk Predcto based o Local Iformato Cosderg the structure relato of IP etwork, lk predcto method based o structure smlarty s more sutable for the predcto of IP etwork topology. There s a premse of assumpto by usg the smlarty of the router odes to predct lk, whch s f the greater the smlarty betwee two routers odes, the the probablty of coecto relato betwee the two odes s bgger. Here, the smlarty maly refers to the proxmty ot the tradto smlarty. o, the core problem to solve s how to defe the smlarty betwee the two odes. Ad from the pot of the etwork coecto, the er router coectg to the edge router (or swtch) s more; the correspodg degree value s bgger. Itutvely, whe choosg the predcto dex cotag weght value chagg wth the degree value chagg, the predcto effectvely s better. Copyrght c 2015 ERC 143
Iteratoal Joural of Grd Dstrbuto Computg 3.1. mlarty Idex The dex of eghbor odes s a smlarty method based o the graph topology, f the tersecto betwee the eghbor set Γ (x) ad Γ (y) of the eghbor ode x ad y s greater, the ode x ad y s more smlar. If for ode z, there s the edge of < x, z > ad < z, y >, so more proe to produce the lk betwee ode x ad y. [6] 3.1.1. Commo Neghbors Idex: (CN) [7] CN dex s the most smple smlarty dex, at the same tme, t oly eeds to cosder the local formato of etwork, theoretcal bass s: f the two odes have the same umber of eghbors, the more lkely exstg coecto edge betwee the two odes. As show Formula (3). ( x ) ( y ) (3) ( x ) ( y ) I IP etwork, are the other routers coected to the router x, are the other routers coected to the router y, f a router z coects to the router x ad y, the, router x may also coects to the router y. 3.1.2. alto Idex: [8] alto Idex formula uses commo eghbor ode umber dvded by the product of the ode degrees. Degree of ode refers to the umber of odes coected wth other eghbors odes. If the ode degree value s bg, to some extet that the hgher the mportace to the odes the etwork. Calculato method s show the Formula (4). ( x) ( y) K K x y (4) 3.1.3. ørese Idex: [9] ørese dex s obtaed by usg commo eghbor umber dvded by the sum of the ode degree; commo ode umber does ot affect the dex value. 2 ( x) ( y) K K x y (5) 3.1.4. Lecht-Holme-Newma Idex: (LHNI) [10] Lecht-Holme-Newma dex focus o that gvg the ode a small weghts f ts adjacet odes has large moderate product. The LHNI dex Formula (6) s lsted below. ( x) ( y) K x K y (6) 3.1.5. Hub Promoted Idex: (HPI) [11] HPI s obtaed by commo eghbor umber dvded by the odes degrees small degree umber. I the adjacet odes, small degree wll get greater weght, odes wth bg degree wll have more beefcal. ( x) ( y) m { K, K } x y (7) 3.1.6. Hub Depressed Idex: (HDI) HDI s opposte to the HPI, whch s to use commo eghbor umber dvded by the large ode degrees, the ode s eghbor s odes, ode wth bg degrees ca get smaller weghts. Because the deomator take bg ode s degrees, odes wth small degree wll ot be domat, therefore, the odes wth bg degree are dsadvatages. 144 Copyrght c 2015 ERC
Iteratoal Joural of Grd Dstrbuto Computg ( x) ( y) m a x { K, K } x y (8) 3.1.7. Adamc-Adar Idex: (AA) [12] AA dex gve all commo eghbor odes small degree to a larger weght. 1 lo g K z ( x ) ( y ) z (9) 3.1.8. Resource Allocato Idex: (RA) [13] RA dex s smlar to AA dex. 1 K z ( x ) ( y ) z (10) 3.1.9. Jaccard Idex: [14] The umber of commo eghbor dvded by the merge set of two odes, whch s dfferet from the ode degree. Whe the ode degree s same, f exstg mult repeated, the hgher the dex s. O the other had, the dex wll reduce. ( x) ( y) ( x) ( y) (11) 3.2. Improvemet Algorthm Desg I chapter 3.1 we troduced the famous lk predcto dex based o the local formato smlarty, order to carry out the IP etwork lk predcto, amog them, commo eghbor smlarty algorthm, cosderg the object s a IP etwork, the router clusterg coeffcet s low, although some odes has o commo eghbors, they are coected by some path, the real smlarty s ot low, but they wll be assged to zero, CN value s sgfcatly lower tha the other dex's AUC. Especally, whe aalyzg the large-scale IP etwork, as the etwork odes s more, usg commo eghbors characters to predct lk by the CN dex, there may be a cosderable umber of odes wth the smlarty score value of 0, whch cause the predcto accuracy s ot hgh. Therefore, assumg the commo eghbor odes wth small degree l ofte larger tha the large degree s more mportat, o the bass of CN, we cosder the fluece of the small commo eghbor odes. o, we adopt the ode of smlarty scores ad combe wth the dex of the AA or RA to the CN dex together to optmze the smlarty dex, combg AA dex wth CN dex s show as follows formula (12). As well as we ca duce the RA dex to the CN dex. Ad s a adjust parameter of (0, 1). ( x ) ( y ) 1 lo g k z ( x ) ( y ) z I addto, the Bayesa classfer may areas have acheved better effect predcto, here, we cosder troduce the ave Bayesa classfer algorthm to the IP etwork lk predcto to judge the IP etwork lk predcto effects. Due to the smple Bayesa classfer s a kd of applcato based o the depedece assumpto of smple Bayesa probablty classfer, order to more accurately descrbe the potetal probablty model as a depedet feature model, a characterstcs set of E(a 1,a 2,...,a ) s (12) Copyrght c 2015 ERC 145
Iteratoal Joural of Grd Dstrbuto Computg gve. Amog them, a s the attrbute value, the probablty of a certa category C uder gve characterstcs of E ca be represeted as codtoal probablty P(C E). [15] P ( C E ) P ( C a, a,..., a ) P ( C ) P ( a, a,..., a C ) P ( a, a,..., a ) Accordg to ave Bayesa theory, above formula (13) ca be expressed as formula (14). (13) P( C ) P ( C E ) P ( a C ) P ( a, a,..., a ) 1 (14) We defe the relatoshp of e for a codtoal probablty uder gve a set of eghbor ode propertes based o the ave Bayesa model algorthm. P ( e ( x, y )) P( e) P ( ( x, y ) e ) P ( ( x, y )) (15) The, we ca separately get the codtoal probablty for exstg e or ot exstg e relatoshp. P( e) P ( e ( x, y )) P ( e,,..., ) P ( e ) P ( ( x, y )) P( e ) P ( e ( x, y )) P ( e,,..., ) P ( e ) P ( ( x, y )) 1 1 (16) (17) Amog them, s a gve eghbor odes of ode par (x, y), so, the smlarty degree of (x, y) may be defed as the rato of (13) ad (14). P ( e ) P ( e ) P( e ) 1 P( e) ( ) P ( e ) P e (18) P ( e ) P ( e ) s 1 P( e) P( e ) The left part of formula (18) s pror codto probablty for a gve IP etworks, because P(e) s a rato of etwork lks ad possble lk. The rght R P( e ) P( e ) part of s the cotrbuto for every eghbor user, so, the CN dex based o the ave Bayesa relato formula (19) s lsted as bellow. ( x, y ) lo g s lo g R ( x, y ) (19) 146 Copyrght c 2015 ERC
Iteratoal Joural of Grd Dstrbuto Computg mlarly, we ca use ave Bayesa relatoshp easy to mprove the dex of AA or RA, etc. 4. Aalyss of Expermet Result We carry out the A coecto lk predcto chapter 2 A coecto dagram of Fgure 1. A show Fgure 1 there are 11 odes ad get the lk par of 11 * 10/2 = 55, but the actual IP etwork ed-to-ed detecto, the actual coecto lk ode par cossts of (1, 5), (1, 6), (5, 6), (1, 2), (2, 7), (2, 8), (3,8), (1, 4), (3, 4), (4, 9), (9, 10), (4, 10), (7, 8) ad (4, 11). Ad some lks could ot obta ther coecto relatoshp. We dvde these actual kow lks to two set, test lk set ad trag lk set through a certa rato value. By usg the above local formato algorthm ad correspodg mprovemet method, we try to predct the lk coecto character. The trag set s expressed as E T ad testg set as E P, the test lk set E P ad those ot bee observed lk (U - E T ) has a smlarty score values core(x, y), sad the possblty sze of the exstg lk betwee x ad y. Accordg to the smlarty algorthm, we get the smlarty score values to all the odes of (x, y), but we do oly pay atteto to the sze of the dscoecto ode pars smlarty scores. That s to say, whe we carry out the ed-toed detecto, f some lk could ot receve the respose formato ICMP packet, ad mssg ths lk coecto formato, through the local smlarty lk predcto we ca obta the most lkely mssg lk. Durg the expermet, we set a certa rato amog the trag set ad testg set, ad take the average to the data of 100 tmes. 4.1. Result of the mlarty Algorthm based o Tradtoal Commo Neghbor The AUC values to dfferet algorthm dex based o local formato commo eghbor algorthm respectvely s show as Table 2. Table 1. AUC Value based o Local Iformato Commo Neghbor Algorthm dex CN alto Jaccard ørese HPI HDI LHN AA RA AUC 0.8967 0.9302 0.9306 0.9308 0.9157 0.9226 0.9309 0.9568 0.957 From the Table 1 commo eghbor smlarty dex we ca see, the predcto accuracy all ca reach above 0.9, whch ca acheve good results. Ad alto, Jaccard, ørese, LHN, AA, ad RA all ca reach about 0.91, whch shows better predcto accuracy. We ca fd the predcto accuracy of dex of AA ad RA are the best two dexes. The predcto accuracy of the PA dex s the worst less tha 0.5, because the defto of PA dex s to gve greater weght to havg bg value of the two odes degrees product. 4.2. Result of Improved Algorthm Model I chapter 3, we put forward a mprovemet method to the dex of CN based o the Bayesa model. Through the expermet, the result of lk predcto (IM_CN) combg wth the AA dex model s 0.9569. The result s lsted at Table 2, form the test result we ca see a obvous mprove, the org predcto result s 0.8967. Ad uder the Bayesa model, the result of CN dex (Bay_CN) s 0.957, whch has ot obvous mproved. Through usg the same method, we try to mprove the Bay_CN algorthm, ad through expermet, the result of mproved Bay_CN (IM_Bay_CN) s 0.9699, whch beyod the etre tradtoal local formato predcto dex. Through aalyss because the Bayesa model formula carry out the stroger Bayesa hypothess to the eghbor role R w, whch represets the other user's cotrbuto to the caddate Copyrght c 2015 ERC 147
Iteratoal Joural of Grd Dstrbuto Computg user are depedet, whch s sutable to the IP etwork ode lk structure, the depedece assumpto coform to the coecto propertes of IP etwork. Therefore, the result after Bayesa hypothess s better tha the tradtoal CN dex, ad through mproved aga, the motor accuracy s hgher tha others. o, the local formato smlarty algorthm based o Bayesa model ad ts mproved s most sutable for the IP etwork lk predcto. Table 2. AUC Value of Improved Algorthm From the Table 2, IM_CN, Bay_CN ad IM_Bay_CN respectvely get mprovemet compare wth the dex of tradtoal local formato predcto dex. The same, the Bayesa model adoptg the mproved method combg wth the dex of AA ca also get some degree mprovemet. I the future work, we wll focus o the complex largescale IP etwork lk predcto, ad verfy the predcto accuracy. I addto, to fd f the method ca be used to the IP etwork mssg lk recovers. 5. Cocluso Through the aalyss ad research to the lk predcto algorthm ad correspodg dex, ad the smulato expermet o the IP etwork model, we ca see from the expermetal results that the local formato smlarty dexes ad ther optmzed dex ca accurately predct the lk coecto. Ad based o the Bayesa depedece assumpto s also sutable to the structure of the IP etwork propertes, ad after troducg mproved dex based o dex of AA or RA to CN, Bay_CN, ad the predcto accuracy ca gas a certa degree mprovemet. Ths paper oly dscuss a kd of fxed A model expermet of IP etwork, from the predcto accuracy ad stablty, the algorthm based o the commo eghbor dex ad ther mproved dex has hgher predcto accuracy, the predcto accuracy ca reach more tha 0.96. As a result, the eghbor algorthm based o the local formato lk predcto dex s sutable to the IP etwork lk predcto. But cosderg the IP etwork structure wth complex coecto, ad especally large-scale IP etwork, t s hard to judge, whether the lk predct ca also obta good results s the future research drecto. Refereces Idex IM_CN Bay_CN IM_Bay_CN AUC 0.9569 0.957 0.9699 [1] R. Rao Kompella, J. Yates, A. Greeberg, A. C. oere, IP Fault Localzato Va Rsk Modelg, 2d ymposum o Networked ystems Desg ad Implemetato, Bosto, Massachusetts, UA, (2005) May 2-4. [2]. Kadula, D. Katab, J-P Vasseur, hrk: A Tool for Falure Dagoss IP Network, IGCOMM'05 Workshops, Phladelpha, PA, UA, (2005) August 22-26. [3] T. Qu, Z. Ge, D. Pe, What Happeed my Network? Mg Network Evets from Router yslogs, IMC 10, Melboure, Australa, (2010) Nov.1-3. [4] X. Xre, Computer Network, Dala Uversty of Techology Press, Dala (2000). p. 174. [5] L. Lyua, Lk Predcto o Complex Networks, Joural of Uversty of Electroc cece ad Techology of Cha,vol. 39, o.5, (2010). pp. 651-660. [6] R. Albert, A L, Barabás, tatstcal mechacs of complex etworks, Revews of moder physcs, vol. 74, o. 1, (2002). p. 47. [7] L.Lu, C.H. J, T. Zhou, mlarty dex based o Local paths for lk predcto of complex etwork, Phys. Rev. E, 80, (2009). [8] G. alto, M J McGll, Itroducto to Moder Iformato Retreval, New York: McDraw-Hll Co., (1983), pp.30-42. [9] T. øreso, A method of establshg groups of equal ampltude plat socology based o smlarty of speces cotet ad ts applcato to aalyses of the vegetato o Dash commos, Bol kr, vol. 5, o.4, (1948). pp. 1-34. 148 Copyrght c 2015 ERC
Iteratoal Joural of Grd Dstrbuto Computg [10] E A Lecht, P. Holme, Newma M E J. Vertex smlarty etworks, Physcal Revew E, vol.73, o.2. (2006). [11] E. Ravasz, A L omera, D A Mogru, et al. Herarchcal orgazato of modularty metabolc etworks, scece, ( 2002), vol. 297, o. 5586, pp. 1553-1555. [12] Adamc L A, Adar E. Freds ad eghbors o the web. ocal Networks, vol. 25, o. 3, (2003), pp.211-230. [13] T. Zhou, L. Lü, Y C. Zhag, Predctg mssg lks va local formato, The Europea Physcal Joural B, vol. 71, o. 4, ( 2009). pp. 623-630. [14] P. Jaccard, Etude comparatve de la dstrbuto florale das ue porto des Alpes et des Jura, Bullet de la ocete Vaudose des cece Naturelles, o. 37, (1901). pp. 547-579. [15] W. Je-hua, Z. A-qg, C. Xue-la, Z. Xao-la, Hdde ave Bayesa model for socal relato recommedato, Applcato Research of Computers, vol. 31, o. 5, (2014). pp. 1382-1383. Authors Che Yu, he s curretly pursug Ph.D. degree from Northwester Polytechcal Uversty, chool of Electrocs ad Iformato. ce 2001, he has bee workg as a teacher Zhegzhou Isttute of Aeroautcal Idustry Maagemet, Departmet of Electroc Commucato ad Egeerg, assstat professor. Hs research terests are crcut ad system, data collecto ad sgal process, etwork formato ad etwork securty, etc. Dua Zhem, he s a professor Northwester Polytechcal Uversty, chool of Electrocs ad Iformato. I 2011, he was awarded a prze of atoal teachg masters. Hs electroc seres basc course teachg team was amed the atoal teachg team 2010. Hs research terests are crcut ad system, data collecto ad sgal process, tegrated crcut aalyss ad desg, electrcal theory ad ew techology, etc. Copyrght c 2015 ERC 149
Iteratoal Joural of Grd Dstrbuto Computg 150 Copyrght c 2015 ERC