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Localized Algorithms and Their Applications in Ad Hoc Networks
Jie WuDept. of Computer Science &
EngineeringFlorida Atlantic University
Boca Raton, FL 33431
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Outline Ad Hoc Wireless Networks Localized Algorithms Three Sample Applications Other Applications Conclusions Future Directions
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(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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Wired/Wireless Networks
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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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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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Unit Disk Graph
A simple ad hoc wireless network of six mobile hosts.
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Characteristics Self-organizing: without centralized control Scarce resources: bandwidth and batteries Dynamic network topology
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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
Major Issues
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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
Major Issues (Cont’d.)
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(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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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 fusion1-hop information2-hop information3-hop information
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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 levels3
3 1
3 1
3
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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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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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Marking Process (Cont’d)
A sample ad hoc wireless network
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Marking Process (Cont’d)
CDS as a virtual backbone0 1 2 3 4 5 6 7 8 9 10
0
1
2
3
4
5
6
7
8
9
10
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(III) Applications in Broadcasting Promiscuous receive mode Coverage & efficiency Flooding: each node forwards the
message once
s
u
v
w
(a)
s
u
v
w
(b)
s
u
v
w
(c)
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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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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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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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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)
timepast view current view
broadcast period
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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)}
Preliminaries: Priority order
s
u
v
wlocal view of w
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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
u
v
w…
replacement path
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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
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A Generic Coverage Condition
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
Theorem 2 (Wu&Dai, ICDCS’03): Theorem 1 still holds when different nodes have different local views
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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
sw(b)
xsource
v u
sw(a)
x
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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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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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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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A Generic Broadcast Scheme Dynamic approach: dependent on the location
of the source and the process of the broadcast process Generic distributed broadcast protocol
1) Periodically v exchanges “hello” messages with neighbors to update local network topology Gk(v).
2) v updates priority information Pr based on snooped/piggybacked messages.
3) v applies the coverage condition to determine its status.
4) If v is a non-forward node then stop.5) v designates some neighbors as forward nodes if
needed and updates its priority information Pr.6) v forwards the packet together with Pr.
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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
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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)
1 2 6
5
7 4
3
1 2 6
5
7 4
3
1 2
5
7
3
1 2
5
7
3
2-hop neighborhoodforward nodecurrent node
47>6>5>4>3>2>1
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Dynamic and Self-Pruning (steps 1, 2, 3, and 6) Special cases:
SBA (Peng&Lu,2000) LENWB (Sucec&Marsic,2000)
1 2 6
5
74
3source
2-hop routing historysourceforward nodecurrent node
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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)
u v
N(v)
N2(u)
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Dynamic and Hybrid (new) Designate one neighbor before applying
the coverage condition
u v
N(v)
N2(u)
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A Sample Broadcasting(n=100, d=6, r=16, k=2)
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(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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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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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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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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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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(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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(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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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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Vision of the Field (Con’t)
Ultimate Cyberinfrastructure Petascale computing, exabyte storage, and terabit
networksNetwork-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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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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Any Questions ?