Multiple Source Multiple. using Network Coding

Transcription

1 Multiple Surce Multiple Destinatin Tplgy Inference using Netwrk Cding Pegah Sattari EECS, UC Irvine Jint wrk with Athina Markpulu, at UCI, Christina Fraguli, at EPFL, Lausanne

2 Outline Netwrk Tmgraphy Gal, Main Ideas, and Cntributins Prpsed Apprach Cnclusin

3 Netwrk Tmgraphy In general Gal: btain a detailed picture f a netwrk frm end-t-end prbes. Infer what? Tplgy, Link-level (lss, delay). Our gal: Tplgy inference, multiple surces, multiple receivers, and intermediate ndes bth netwrk cding and multicast.

4 Tw bdies f related wrk Netwrk Tmgraphy Inference with Netwrk Cding Multicast trees using lss crrelatins Unicast prbes Active prbing, reliance n the number, rder, delay variance and lss f received prbes, and heuristic r statistical signalprcessing apprach. Mstly related: Rabbat, Cates, Nwak, Multiple-Surce Internet Tmgraphy, IEEE JSAC 06. Passive Failure patterns [H et al., ISIT 05] Tplgy inference [Sharma et al., ITA 07] Bttleneck discvery/verlay management in p2p [Jafarisiavshani et al., Sigcmm INM 07] Subspace prperties [Jafarisiavshani et al., ITW 07] Active Lss tmgraphy [Gjka et al., IEEE Glbecm 07] Binary tree inference [Fraguli et al., Allertn 06]

5 Main idea 1 Netwrk cding: tplgy-dependent crrelatin [Fraguli et al., 2006], [Sharma et al., 2007] Netwrk cding intrduces tplgy-dependent crrelatin amng the cntent f prbe packets, which can be reverse- engineered t infer the tplgy. Netwrk cding can make the packets stay tgether and reveal the cding pint. x 1 x 2 x 1 +x 2

6 Main idea 2 General Graphs (DAG) An M-by-N DAG, with a given ruting plicy that has three prperties: A unique path frm each surce t each destinatin. All 1-by-2 cmpnents: inverted Y. All 2-by-1 cmpnents: Y. Cnsistent with the ruting in the Internet. Lgical tplgy. branching pint S S 1 S 2 B J jining pint R 1 R 2 R Nt a lgical tplgy!

7 Main Idea 2, Cnt d 2-by-2 Cmpnents Rabbat et al., 2006 A traditinal multiple surce, multiple receiver tmgraphy prblem can be decmpsed int multiple tw surce, tw receiver sub-prblems. Fur 2-by-2 types. S 1 S 2 S S 1 2 S 1 S 2 S 1 S 2 B B 2 2 B J 1 =J 2 =J J J B 1 =B 2 =B B 1 B 1 B 1 J 2 J 1 J 1 J 2 R 1 R 2 R 1 R 2 R 1 R 2 R 1 R 2 Type 1:shared Type 2:nn-shared Type 3:nn-shared Type 4:nn-shared

8 Main Idea 2, Cnt d Decmpsitin int 2-by-2 S 1 S 2 S 1 S 2 S 1 S 2 B J 1 =J 2 2 Decmpsitin J 1=J 2 J 1 =J 2 B 2 S 1 S 2 B 2 J 1 =J 2 B 1,2 B 1,2 B 2,3 J 3 B 12 1,2 J 3 B 2,3 J 3 R 1 R 2 R 3 R 1 R 2 R 1 R 3 R 2 R 3

9 Previus Wrk 2-by-2 s and Merging g Rabbat et al., Δ Δ 2 1 S 1 S 1 S 2 randm B ffset 2 J S 2 J 8 B B 8,9 R 1 R Δ Δ 1 2 randm ffset J J 2 1 B 17 1,7 B 3,5 J 1 J 1 J 3 J 5 J 7 B 1,2 B 3,4 B 5,6 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 1 R 3

10 Weaknesses f Previus Wrk In the 2-by-2 2 inference step, they can nly distinguish between type 1 (shared) and types 2,3,4 234 (nn-shared) shared). This results in inaccurate identificatin f the jining pint lcatins in the merging step. I.e., bunds within a sequence f several cnsecutive lgical links.

11 Our Cntributins At the 2-by-2 2 inference step: Netwrk cding helps us distinguish amng all fur 2-by-2 types by lking at the cntent. At the merging step: Under the same assumptin as in prir wrk (S 1 1-by-N), we can lcalize each jining pint, fr each receiver, t a single lgical link. In additin, we can als design anther merging algrithm, withut t such an assumptin, and by nly using the 2-by-2 infrmatin.

12 Outline Netwrk Tmgraphy Gal, Main Ideas, and Cntributins Prpsed Apprach Assumptins, Nde Operatins Step 1: 2-by-2 2 Cmpnents (lssless/lssy) Step 2: Merging Algrithms (tw scenaris) Simulatin Results Cnclusin

13 Assumptins Delay: fixed part (prpagatin) and randm part (queuing); independent acrss links. Packet lss: bth lssless and lssy cases. Carse synchrnizatin (~5-10ms) acrss ndes. achievable via a handshaking scheme, e.g., NTP. We design active prbing schemes, i.e., the peratin f surces, intermediate ndes and receivers, which allw tplgy inference frm the bservatins.

14 Nde Operatins Surces: synchrnized later relaxed by large time windw W in sme algrithms, an artificial ffset u up t cuntmax experiments, spaced by time T. Jining pint: adds and frwards packets within W (additins ver Fq). x 1 =[1,0] S S 1 2 x 2 =[0,1] J 1 B 1 B 2 J 2 R 1 R 2 Branching pint: frwards the single received packet t all interested links dwnstream (the next hp fr at least ne surce packet in the netwrk cde).

15 Nde Operatins Surces: synchrnized later relaxed by large time windw W in sme algrithms, an artificial ffset u up t cuntmax experiments, spaced by time T. Jining pint: adds and frwards packets within W (additins ver Fq). x 1 =[1,0] S S 1 2 x 2 =[0,1] J 1 B 1 B 2 J 2 R 1 R 2 Branching pint: frwards the single received packet t all interested links dwnstream (the next hp fr at least ne surce packet in the netwrk cde).

16 Nde Operatins Surces: synchrnized later relaxed by large time windw W in sme algrithms, an artificial ffset u up t cuntmax experiments, spaced by time T. Jining pint: adds and frwards packets within W (additins ver Fq). x 1 =[1,0] S S 1 2 x 2 =[0,1] J 1 B 1 B 2 J 2 R 1 R 2 c 11 x 1 +c 12 x 2 c 21 x 1 +c 22 x 2 Branching pint: frwards the single received packet t all interested links dwnstream (the next hp fr at least ne surce packet in the netwrk cde).

17 Outline Netwrk Tmgraphy Gal, Main Ideas, and Cntributins Prpsed Apprach Assumptins, Nde Operatins Step 1: 2-by-2 2 Cmpnents (lssless/lssy) Step 2: Merging Algrithms (tw scenaris) Simulatin Results Cnclusin

18 Inferring 2-by-2 s 2s, N Lss Distinguishing amng {1,4}, 2 r 3 R 1 R 2 R 1 R 2 R 1 R 2 R 1 R 2 x 1 +x 2 x 1 +x 2 x 1 +x 2 x 1 +2x 2 x 1 +2x 2 x 1 +x 2 x 1 +x 2 x 1 +x 2 One prbe distinguishes amng Types: {1,4}, 2 r 3.

19 Inferring 2-by-2 s 2s, N Lss Distinguishing between 1,4 Type 1: J 1 =J 2 =J. Type 4: J 1,J 2 different. Can be achieved by Apprpriately selecting u.

20 Inferring 2-by-2 s 2s, N Lss Selecting the apprpriate ffset S 1 S 2 B 2 W-D 1 W-D 2 W-D 2 W-D 1 D 1 D 2 0 W 0 W J 1 B 1 R 1 R 2 J R 1 : x 1 R 1 : 2 x 1 +x 2 R 2 : x 1 +x 2 R 2 : D 1>D 2 Type (4) tplgy 2, D 1 <D 2, ffset frm [W-D 1,W-D 2 ] ffset frm [W-D 2,W-D 1 ] x 1 2-by-2 s: 2s: u є [W-D 1,W-D 2 ] Mre general: u є [0,W]

21 Inferring 2-by-2 s 2s, Lssy Case R 1 R 2 R 1 R 2 R 1 R 2 R 1 R 2 x 1 x 1 x 1 +x 2 x 1 +x 2 x 1 x 1 x 1 +x 2 - meetings n lnger guaranteed, bservatins n lnger predictable! There are cmmn bservatins acrss all 4 types. Each experiment might result in different utcmes.

22 Inferring 2-by-2 s 2s, Lssy Case All pssible bservatins There are three grups f bservatins: (i) at least ne receiver des nt receive any packet (-), (ii) R 1 = R 2, (iii) R 1 R 2.

23 Inferring 2-by-2 s 2s, Lssy Case Sme bservatins f grup (iii) help! E.g., c 12 -c 22 <0 can nly ccur fr type 2 r 4! c 12 -c 22 >0 can nly ccur fr type 3 r 4,

24 Inferring 2-by-2 s 2s, Lssy Case Try t create grup (iii) bservatins! Either naturally (lss) r artificially (u). Especially fr small lss rates and like the lssless case: u є [0,W]

25 Inferring all 2-by-2 s in a 2-by-N Imprtant fr the merging algrithm. 2 surces multicast t N receivers. Additins ver a larger field. Algrithms can be applied t any pair f receivers amng all N chse 2 pssible pairs. S 2 x 2 =[0,1] S 1 x 1 =[1,0] B 2 x 2 J 1 B 3,4 B 17 1,7 B 3,5 B 8,9 B 5,6 J 8 J 3 J 5 J 7 B 1,2 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 x1+2x2 x1+x2

26 Advantages ver Prir Wrk Mre accurate: we can distinguish amng all fur 2-by-2 types. Faster One bservatin that uniquely characterizes the 2-by-2 type is sufficient. Unlike [Rabbat et al.], we d nt need many experiments fr statistical significance. Less Bandwidth verhead Duplicate packets crssing the same link.

27 Outline Netwrk Tmgraphy Gal, Main Ideas, and Cntributins Prpsed Apprach Assumptins, Nde Operatins Step 1: 2-by-2 2 Cmpnents (lssless/lssy) Step 2: Merging Algrithms (tw scenaris) Simulatin Results Cnclusin

28 Merging Step Using the 2-by-2 2 infrmatin, we design tw merging algrithms t infer the 2-by-N structure under tw scenaris: 1. Assuming knwledge f a 1-by-N tree tplgy (e.g., using classic tmgraphy methds). We can slve exactly (previusly apprximately slved). 2. N 1-by-N tree tplgy is given. We can als slve (previusly impssible). We then generalize ur apprach t the M- by-n netwrk.

29 S 2 Merging g Algrithm 1 S 1 1-by-N given Given: 2-by-2 s and S 1 s 1-by-N. S 2 S 1 J 8 J 1 =J 2 B 8,9 B 17 B 1,2 1,7 R 1 R 2 J 1 B 3,4 B 3,5 S 2 J 3 J 5 J 7 B B 1,7 1,2 B 5,6 J 1 J 7 S 1 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 1 R 7

30 Merging g Algrithm 2 n 1-by-N given Only the 2-by-2 s are given. S 2 S 1 B 1,3 J J 3 J 1 J 5 8 J B B B 1,2 3,4 B 7 5,6 8,9 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9

31 Cmparisn f the tw algrithms S 2 Merging Alg. 1 S 2 Merging Alg. 2 S 1 S 1 J 8 J 8 B 8,9 B 8,9 B 1,7 B 3,5 B 1,2 J 1 J 3 J J 5 1 J J 3 J 5 7 J7 B 3,4 B B 5,6 B 1,2 B 3,4 B 5,6 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9

32 Frm 2-by-N t M-by-N 2-by-N can be directly extended t M-by-N. Starting frm a 2-by-N tplgy, we add ne surce at a time, t cnnect the remaining M-2 surces. Assume we have cnstructed a k-by-n tplgy, 2<=k<M: T add the (k + 1) th surce, we perfrm k experiments: At each experiment ne different f the k surces and the (k+1) th surce send packets x 1 and x 2. We then glue these tplgies tgether by fllwing the tplgical rules previusly described.

33 Outline Netwrk Tmgraphy Gal, Main Ideas, and Cntributins Prpsed Apprach Assumptins, Nde Operatins Step 1: 2-by-2 2 Cmpnents (lssless/lssy) Step 2: Merging Algrithms (tw scenaris) Simulatin Results Cnclusin

34 Simulatin Setup Tplgy Rabbat et al.,2006 An Internet tplgy cnnecting hsts at academic institutins in the US and Eurpe. S 2 J 8 B 8,9 B 17 1,7 B 3,5 J 1 J 1 J 3 J 5 S 1 B 1,2 J 7 B 3,4 B 5,6 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9

35 Simulatin Results Absence f lss Presence f lss cuntmax=50 cuntmax=100 cuntmax= % err r % err r number f experiments (cuntmax) Errr: type 4 as type 1. Errr prb.~0 in cuntmax~50 Prev. Wrk: type 1 (shared) vs. {2,3,4} (nn-shared) % lss (same n every link) Errr: types 2,3,4 as type 1 r type 4 as type 2 r 3. Errr prb. decreases rapidly with cuntmax. Prev. wrk: 1000 prbes (nly type 1, {2,3,4}), lss~2%, errr 5-10%.

36 Cnclusin Summary Tmgraphic techniques fr tplgy inference in a netwrk with netwrk cding. Future directins Likelihd f the bservatins. Structures larger than 2-by-2: Mre than tw surces and tw receivers. E f h f Expect a faster merging step at the cst f a mre cmplicated inference step.