1. Localized Algorithms and Their Applications in Ad Hoc Networks
Jie Wu
Dept. of Computer Science & Engineering
Florida Atlantic University
Boca Raton, FL 33431
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2. Outline Ad Hoc Wireless Networks Localized Algorithms
Three Sample Applications
Other Applications
Conclusions
Future Directions
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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)
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4. Wired/Wireless Networks
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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"
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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
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7. Unit Disk Graph A simple ad hoc wireless network of six mobile hosts.
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8. Characteristics Self-organizing: without centralized control
Scarce resources: bandwidth and batteries
Dynamic network topology
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9. Major Issues Mobility management Location tracking Network 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
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10. Major Issues (Cont’d.) MAC protocols Applications and middleware
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
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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.
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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
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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
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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
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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).
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16. Marking Process (Cont’d)
A sample ad hoc wireless network
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17. Marking Process (Cont’d)
CDS as a virtual backbone
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18. (III) Applications in Broadcasting
Promiscuous receive mode
Coverage & efficiency
Flooding: each node forwards the message once u s u v w
(a) u s w s w v v
(c)
(b)
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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
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20. Classification Probabilistic vs. Deterministic*
Deterministic algorithms: forward nodes (including the source) form a CDS
Non-localized vs. Localized*
Self-pruning* vs. Neighbor-designating*
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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
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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
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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 s w v
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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
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25. A Generic Coverage Condition
Theorem 1 (Wu&Dai, Infocom’03): Forward node set V’ derived based on the coverage condition forms a CDS
Proof:
Each pair of nodes u and v are connected via forward nodes
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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
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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)
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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
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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)
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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.
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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.
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32. Existing Protocols as 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
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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 1 1
2-hop neighborhood
forward node 5 5 5 5
current node 3 3 3 3
7>6>5>4>3>2>1 7 7 7 7 4 4 4
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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
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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
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36. Dynamic and Hybrid (new)
Designate one neighbor before applying the coverage condition
N2(u)
N(v) u v
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37. A Sample Broadcasting (n=100, d=6, r=16, k=2)
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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
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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
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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
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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)
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42. Open Issues Complexity and Efficiency Tradeoffs Mobility Management
Extensibility to other Models
Directional antenna
Hitchhiking model …
Other Applications
Localized security
Localized incentive mechanisms
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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
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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
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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
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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
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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)
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48. Any Questions ?
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