Computational Geometry in Wireless Networks - Routing. Presented by Heather M. Michaud

Transcription

1 Compaional Geomery in Wireless Neworks - Roing Presened by Heaher M. Michad 1

2 Ad Hoc Wireless Neworks No fixed pre-exising infrasrcre Nodes can be saic or mobile Assme nodes don move dring roing or opology consrcion Decenralized Each node paricipaes in roing (hos or roer) Nodes have limied baery & memory 2

3 Ad Hoc Wireless Neworks Every node can commnicae wih anoher wihin one or more hops Each node has a ransmission range and GPS A node v can receive a packe from a sender node if i is wihin he ransmission range of node 3

4 Uni Disk Graph (UDG) The se of wireless nodes represens a UDG(V) of n nodes All nodes have eqal ransmission range and an omnidirecional anenna (forms disk) If disance beween nodes is 1 (disks have non-empy inersecion), hen here is an edge beween hem Assme he UDG is a leas biconneced o garanee fal olerance 4

5 Uni Disk Graph (UDG) The UDG can be as large as n 2 ; we wan o consrc a sbgraph of he UDG ha: is sparse can be consrced locally and efficienly is sill good compared o he original UDG w.r.. roe qaliy 5

6 Wha we wan in he UDG sbgraph Aracive nework feares bonded node degree low srech facor (shores pah beween nodes in sbgraph is no mch longer han in he original) linear nmber of links Aracive roing schemes localized roing wih garaneed performance 6

7 Roing Table-driven proocols mainain a able of p o dae info on he opology of nework explici roe mainenance is expensive in commnicaion and memory does no scale Demand-driven proocols only creae roes when demanded by sorce node roe discovery is expensive, redces response ime Localized roing proocols se he geomeric nare of nework o creae roes 7

8 Localized Roing Proocols niform - all nodes exece he same proocol when deciding which node o forward a packe nodes don mainain ables, less overhead scalable challenging o design no bil-in way o avoid congesion by overloading nodes 8

9 Localized Roing Proocols A roing proocol is localized if he decision on which node o forward a packe o is based only on: informaion in he packe header (e.g. sorce & desinaion) local informaion gahered by he node from a small neighborhood (e.g., se of 1-hop neighbors) 9

10 Localized Algorihm Becase nodes have limied resorces, i s preferred ha he nderlying nework opology is consrced wih a localized algorihm A graph consrcion algorihm is localized if every node can exacly decide all edges inciden on based only on he informaion of all nodes wihin consan hops of. Localized algorihms: YG(V), RNG(V), GG(V) No localized algorihms: EMST(V), Del(V) 10

11 Locaion Service - Where does a packe go? Mobile nodes regiser heir locaions o he locaion service. The sorce node has o learn he crren locaion of he desinaion node. When a sorce node doesn know he posiion of he desinaion node, i qeries he locaion service For caegories: some-for-all (some nodes sore posiions of all oher nodes) some-for-some (e.g., a qorm - some nodes are represenaives for ohers) all-for-some all-for-all 11

12 Localized Roing Assmpions Nodes know heir Eclidean locaions heir 1-hop neighbors he Eclidean locaion of he desinaion Nodes are qasi-saic Nodes can keep some exra info if needed 12

13 Localized Roing Proocols Sraegies on how o decide which neighbor o forward he packe o Don garanee delivery in arbirary graph Compass Roing Greedy Roing Greedy-Compass Random Compass Roing Mos Forward Roing Neares Neighbor Roing Farhes Neighbor Roing Garanee delivery IF working on Del(V) Garanee delivery in planar graphs Face Roing Greedy Perimeer Saeless Roing 13

14 Compass Roing Le be he desinaion node. Crren node forwards a packe o node v whose angle v is he smalles among all neighbors of v No garaneed delivery (nless working on a Delanay Trianglaion) 14

15 Compass Roing v 15

16 Compass Roing v 16

17 Compass Roing v 17

18 Compass Roing v 18

19 Compass Roing 19

20 Random Compass Roing Randomly selec eiher v 1 or v 2 o forward he packe o v 1 is he node wih he smalles v 1 among all neighbor nodes above he line v 2 is he node wih he smalles v 2 among all neighbor nodes below he line v1 v2 No garaneed delivery 20

21 Random Compass Roing v1 v2 21

22 Random Compass Roing v1 v2 22

23 Random Compass Roing v1 v2 23

24 Random Compass Roing v2 v1 24

25 Random Compass Roing v1 v 2 25

26 Random Compass Roing v2 v1 26

27 Random Compass Roing 27

28 Greedy Roing Forward packe o node v sch ha he disance v is he smalles among all neighbors of v No garaneed delivery (nless working on a Reglar Trianglaion) 28

29 Greedy Roing v 29

30 Greedy Roing v 30

31 Greedy Roing v 31

32 Greedy Roing 32

33 Greedy-Compass Roing Find he neighbors v 1 and v 2 sch ha v 1 forms he smalles coner-clockwise angle v 1 among all neighbors v 2 forms he smalles clockwise angle v 2 among all neighbors Forward o eiher v 1 and v 2 based on who has minimm disance o v1 v2 No garaneed delivery (nless working on Any Trianglaion) 33

34 Greedy-Compass Roing v1 v2 34

35 Greedy-Compass Roing v1 v2 35

36 Greedy-Compass Roing v1 v2 36

37 Greedy-Compass Roing 37

38 Mos Forwarding Roing (MFR) Forward o node v sch ha v is he smalles among all neighbors, where v is he projecion of v on segmen v v No garaneed delivery 38

39 Mos Forwarding Roing (MFR) v1 39

40 Mos Forwarding Roing (MFR) v v1 40

41 Mos Forwarding Roing (MFR) v1 41

42 Mos Forwarding Roing (MFR) 42

43 Neares Neighbor Roing (NN) Given a parameer angle α, forward he packe o he neares node v sch ha v α v No garaneed delivery 43

44 Neares Neighbor Roing (NN) 44

45 Neares Neighbor Roing (NN) 45

46 Neares Neighbor Roing (NN) 46

47 Neares Neighbor Roing (NN) 47

48 Neares Neighbor Roing (NN) 48

49 Neares Neighbor Roing (NN) 49

50 Farhes Neighbor Roing (FN) Given a parameer angle α, forward he packe o he farhes node v sch ha v α v No garaneed delivery 50

51 Farhes Neighbor Roing (FN) 51

52 Farhes Neighbor Roing (FN) 52

53 Farhes Neighbor Roing (FN) 53

54 Farhes Neighbor Roing (FN) 54

55 Farhes Neighbor Roing (FN) 55

56 Localized Roing Proocols 56

57 Roing Qaliy Measres A measre of roing qaliy is based on Garaneed delivery Minimize oal Eclidean disance raveled Minimize oal power consmed 57

58 No all proocols garanee delivery E.g., greedy forwarding can ge sck a a local minimm 58

59 Theorem 5.1 When packe delivery is garaneed, based on proocol and he nderlying opology Any opology Any Trianglaion Reglar Trianglaion Delanay Trianglaion Greedy NO NO NO YES Compass NO NO YES YES Greedy-Compass NO YES YES YES Random-Compass NO NO NO NO Mos-Forwarding Roing NO NO NO NO Neares Neighbor NO NO NO NO Farhes Neighbor NO NO NO NO 59

60 Meric comparison None garanee a consan raio of he pah compared wih he minimm 60

61 Face Roing (Planar Graph Roing) Used in planar graphs Packe is forwarded along he face bondaries inerseced by he line segmen beween he sorce and desinaion nodes Garanees delivery Uses righ-hand rle (walk nex clockwise edge, raverse face conerclockwise) z Garanee delivery x y 61

62 Face Roing (Planar Graph Roing) F2 F3 F1 F4 F5 62

63 Greedy Perimeer Saeless Roing (GPSR) GPSR = Greedy Roing + Face Roing Main sraegy is greedy roing When a node is closer o he desinaion han any of is neighbors, face roing is sed as a recovery Garaneed delivery Garanee delivery 63

64 Greedy Perimeer Saeless Roing (GPSR) Greedy algorihm fails becase x is closer o D han w and y are. Swich o face roing (x -> y -> z -> D) 64

65 References (1) Li, Xiang-Yang. "Applicaions of compaional geomery in wireless ad hoc neworks." Ad Hoc Wireless Neworking. Klwer (2003): (2) Li, Xiang-Yang. "Topology conrol in wireless ad hoc neworks." Mobile Ad Hoc Neworking (2003): (3) Karp, Brad, and Hsiang-Tsng Kng. "GPSR: Greedy perimeer saeless roing for wireless neworks." Proceedings of he 6h annal inernaional conference on Mobile comping and neworking. ACM, (4) hps://en.wikipedia.org/wiki/uni_disk_graph (5) hp://www3.cs.sonybrook.ed/~jgao/cse590-fall09/georoing.pdf 65