Localized Algorithms and Their Applications in Ad Hoc Networks

1. Localized Algorithms and Their Applications in Ad Hoc Networks Jie Wu Dept. of Computer Science & Engineering Florida Atlantic University Boca Raton, FL 33431

2. Outline • Ad Hoc Wireless Networks • Localized Algorithms • Three Sample Applications • Other Applications • Conclusions • Future Directions

3. (I) Ad Hoc Wireless Networks • Wired Networks • LAN, MAN, WAN, and Internet • Wireless Networks • Infrastructured networks (cellular networks) • Infrastructureless networks (ad hoc wireless networks)

4. Wired/Wireless Networks

5. Wireless Networks • 200 million wireless telephone handsets (purchased annually) • A billion wireless communication devices in use • The first decade of 21st Century: mobile computing • "anytime, anywhere"

6. Ad Hoc Wireless Networks (Infrastructureless networks) • MANETs(mobile ad hoc networks) • No base station and rapidly deployable • Neighborhood awareness • Multiple-hop communication • Unit disk graph: host connection based on geographical distance

7. Unit Disk Graph A simple ad hoc wireless network of six mobile hosts.

8. Characteristics • Self-organizing: without centralized control • Scarce resources: bandwidth and batteries • Dynamic network topology

9. Major Issues • Mobility management • Addressing and routing • Location tracking • Absolute vs. Relative, GPS • Network management • Merge and split • Resource management • Network resource allocation and energy efficiency • QoS management • Dynamic advance reservation and adaptive error control techniques

10. Major Issues (Cont’d.) • MAC protocols • Contention-base, controlled • Applications and middleware • Measurement and experimentation • Security • Authentication, encryption, anonymity, and intrusion detection • Error control and failure • Error correction and retransmission, deployment of back-up systems

11. (II) Localized Algorithms (Estrin, 1999) • Processors (hosts) only interact with others in a restricted vicinity. • Each processor performs exceedingly simple tasks (such as maintaining and propagating information markers). • Collectively these processors achieve a desired global objective. • There is no (or limited) sequential propagation of information.

12. Local information • k-hop information • Discovered via k rounds of Hello exchanges • Topology and other information • Usually k=1, 2, or 3 • Information gathering vs. information fusion 1-hop information 2-hop information 3-hop information

13. Application I: Safety Level(Wu, 1992) • Safety level (fault-tolerant comm. in hypercubes) • Approximation of routing capability of a node in faulty hypercubes • Safety level as a function of neighbors’ safety levels 3 1 3 3 3 1

14. Application II: Virtual Backbone Formation • Applications include topology management, coverage & routing • Requirements include connectivity, size, formation overhead, routing distance, etc • Using a connected dominating set (CDS) as a virtual backbone • Each node has at least one neighbor in VB • Each pair of nodes can communicate via VB

15. Marking Process (Wu and Li, 1999) • A node is marked true if it has two unconnected neighbors. • Marked node sets (gateway nodes) form a connected dominating set (CDS).

16. Marking Process (Cont’d) A sample ad hoc wireless network

17. Marking Process (Cont’d) CDS as a virtual backbone

18. u w s v (a) (III) Applications in Broadcasting • Promiscuous receive mode • Coverage & efficiency • Flooding: each node forwards the message once u u w s w s v v (c) (b)

19. Motivation & Objectives • Objective: determine a small set of forward nodes to ensure coverage in a localized way • Existing works: different assumptions and models • A generic framework to capture a large body of protocols • One proof for the correctness of all protocols • Address various assumptions/techniques • Combine techniques to achieve higher efficiency

20. Classification • Probabilistic vs. Deterministic* • Deterministic algorithms: forward nodes (including the source) form a CDS • Non-localized vs. Localized* • Self-pruning* vs. Neighbor-designating*

21. Preliminaries: View • Unit disk graph: ad hoc network • G= (V, E) • View: a snapshot of network topology and broadcast state • View(t) = (G, Pr(V, t)) • Priority: (forwarding status, id) • Pr(v, t) = (S(v,t), id(v)), v є V

22. Preliminaries: Forwarding status • Forwarding status: time-sensitive • forward node vs. non-forward node • Local view: View’, partial view within vicinity • visible node vs. invisible node (level: 0) • G’ is a subgraph of G and Pr’(V) < Pr(V) broadcast period time past view current view

23. Preliminaries: Priority order • Pr(v) > Pr(u) based on lexicographical order: • visited (2) > unvisited (1) > invisible (0) • Global view: {(2, s), (1, u), (2, v), (1, w)} • Local 1-hop view of w: {(0, s), (1, u), (2, v), (1, w)} u local view of w w s v

24. A Generic Coverage Condition • Node v has a non-forwarding status if • For any two neighbors u and w, a replacement path consisting of nodes with higher priorities than that of v exists replacement path u w … v

25. A Generic Coverage Condition Proof: Theorem 1(Wu&Dai, Infocom’03): Forward node set V’ derived based on the coverage condition forms a CDS Each pair of nodes u and v are connected via forward nodes

26. A Generic Coverage Condition Theorem 2 (Wu&Dai, ICDCS’03): Theorem 1 still holds when different nodes have different local views Proof: • Forward status fi(vi)i is computed from G(vi) and Pri(V) • Assume fsuper (vi) is computed from a global view • Gsuper = (V(v1)  V(v2) ...  V(vn), E(v1)  E(v2) ...  E(vn)) • Prsuper (vi) = max{Pr1(vi), Pr2(vi), ..., Prn(vi)} • We have fi(vi)fsuper (vi) and {vi|fsuper (vi)=1} is a CDS • Therefore, {vi|fi(vi)=1} is a CDS

27. Timing Issues • Static:decision before the broadcast process • Dynamic:decision during the broadcast process • First-receipt • First-receipt-with-backoff s>u>v>x>w v u x v u x source w s w s (a) (b)

28. Selection Issues • Self-pruning: v’s status determined by itself • Neighbor-designating: v’s status determined by its neighbors • Hybrid: The status of v is determined by v and its neighbors

29. Space Issues • Network topology information (long lived) • Periodic “hello” message • K-hop neighborhood information (k=2 or 3) • Broadcast state information (short lived) • Snooped: snoop the activities of its neighbors • Piggybacked: attach h most-recently visited node information (including designated forward neighbors)

30. Priority Issues • Pr(v): (forward status, id) • 0-hop priority: id(v) • 1-hop priority: deg(v) • 2-hop priority: ncr(v) • ncr (neighborhood connectivity ratio): the ratio of pairs of neighbors that are not directly connected to pairs of any neighbors.

31. A Generic Broadcast Scheme • Dynamic approach: dependent on the location of the source and the process of the broadcast process • Generic distributed broadcast protocol Periodically v exchanges “hello” messages with neighbors to update local network topology Gk(v). v updates priority information Pr based on snooped/piggybacked messages. v applies the coverage condition to determine its status. If v is a non-forward node then stop. v designates some neighbors as forward nodes if needed and updates its priority information Pr. v forwards the packet together with Pr.

32. Existing Protocols as Special Cases • Special cases • Skipping some steps • A strong coverage condition (step 3) • Designated forward node selections (step 5) • Strong coverage condition • v is non-forwarding if it has a coverage set • The coverage set belongs to a connected component of nodes with higher priorities than that of v • Complexity: O(D2)compared with O(D3), where D is density

33. Static Algorithms (steps 1 and 3) • Special cases: • Marking process with Rules 1 &2 (Wu&Li, DiaLM’99) • Marking process with Rule k (Dai&Wu,ICC’03) • Span (Chen et al, MobiCom’01) 2 2 2 2 1 1 6 6 2-hop neighborhood 1 1 forwardnode 5 5 current node 5 5 3 3 3 3 7>6>5>4>3>2>1 7 7 7 7 4 4 4

34. Dynamic and Self-Pruning (steps 1, 2, 3, and 6) • Special cases: • SBA (Peng&Lu,2000) • LENWB (Sucec&Marsic,2000) 2 1 6 2-hop routing history source source 5 3 forward node current node 7 4

35. Dynamic and Neighbor Designating (steps 1,2,4,5,and 6) • Special cases: • Multipoint relay (MPR) (Qayyum et al, 2002) • Dominant pruning (Lim&Kim, 2001) • Total/partial dominant pruning (Lou&Wu, 2003) N2(u) N(v) u v

36. Dynamic and Hybrid (new) • Designate one neighbor before applying the coverage condition N2(u) N(v) u v

37. A Sample Broadcasting(n=100, d=6, r=16, k=2)

38. (IV) Other Applications • Energy-efficient design and power-aware routing/broadcasting • Reducing computation complexity • Maximizing the traffic capacity • Reducing power consumption • Prolonging the life span of each node • Reducing MAC-layer power consumption

39. Other Applications (Con’t) • Topology Control • Localized solutions • Location-aware solutions • Localized Delaunay triangulation, Gabriel, Yao, RNG graphs … • MAC Layer Protocols • Variable transmission ranges • Directional antenna

40. Other Applications (Con’t) • Sensor Networks • Coverage problem • Exposure problem • Data dissemination and gathering • Dynamic sensor deployment • Peer-to-peer Networks • Localized and scalable solutions for the look-up problem

41. Some New Results • Safety Level: Efficient solutions to handle link faults (IEEE TR 2004) • CDS: Computation complexity reduction in dense mode (ICDCS 2004) • Broadcast: Mobility management and consistent view (INFOCOM 2004)

42. Open Issues • Complexity and Efficiency Tradeoffs • Mobility Management • Extensibility to other Models • Directional antenna • Hitchhiking model • … • Other Applications • Localized security • Localized incentive mechanisms • …

43. (V) Conclusions • Localized Algorithms • Approximation for optimization problems • Simple and scalable design • Self-organizing, self-stabilizing, and self-healing • Applications in dynamic systems • Ad hoc wireless networks • Sensor networks • Peer-to-peer networks

44. (VI) Future Directions • Cross Disciplinary Efforts • NSF Sensor Network Program (March, 2003):Sponsored by multiple divisions/programs • Encouraging multi-disciplinary team effort • Hitch-hiking Model Energy-efficient design in sensor networks (UMass- FAU, INFORCOM 2004) • Multiple disciplines • physical layer • MAC layer • network layer

45. Vision of the Field • Convergence of Multiple Disciplines • Parallel processing • Distributed systems • Network computing • Wireless network and mobile computing as an important component in Cyberinfrastructure and Cybertrust

46. Vision of the Field (Con’t) Ultimate Cyberinfrastructure • Petascale computing, exabyte storage, and terabit networks Network-Centric • Supernetworks: networks are faster than the computers attached to them • Endpoints scale to bandwidth-match the network with multiple-10Gbps lambdas

47. Major Conferences in the Fields • General: IEEE INFOCOM • Mobile Computing: ACM MobiCom • Ad Hoc Networks: ACM MobiHoc • Distributed Systems: IEEE ICDCS • Sensor Networks:IEEE MASS (Mobile Ad-hoc and Sensor Networks)

48. Any Questions ?