1 Distributed Navigation Algorithms for Sensor Networks Chiranjeeb Buragohain, Divyakant Agrawal, Subhash Suri Dept. of Computer Science, University of.

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Distributed Navigation Algorithms for Sensor Networks

Chiranjeeb Buragohain, Divyakant Agrawal, Subhash Suri

Dept. of Computer Science, University of California, Santa Barbara, CA 93106, USA

IEEE INFOCOM 2006

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Outlines

Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results Conclusions

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Main ideas

Distributed algorithms to aid navigation of a user through area covered by sensors.

Danger zone, danger point, safe path Flooding (optimal) vs. reduced graph (approximately

optimal ) Basic solution

Construct a reduced graph Carry out a search on the skeleton graph to find shortest

path/minimal exposure paths over the skeleton graph only

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Previous works

GPSR (Greedy Perimeter Stateless Routing) Local search Low communication cost, but low performance Stateless is not meant literally, but refers to this

small, purely local state. Flooding

Global search High performance, but high communication cost

[9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM 2000.

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References [8] Q. Li, M. DeRosa, and D. Rus, “Distributed algorithms for guid

ing navigation across a sensor network,” in Proc. of IPSN ’03., 2003.

[9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM 2000.

[14] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, “Exposure in wireless ad-hoc sensor networks,” in Proc. of MOBICOM 2001, 2001.

[15] G. Veltri, Q. Huang, G. Qu, and M. Potkonjak, “Minimal and maximal exposure path algorithms for wireless embedded sensor networks,” in Proc. of SenSys 2003, 2003.

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Danger Zone Shortest feasible path

Danger Point Minimum exposure path

Probability of detection

where

R is the Euclidean distance from the point of dangerto the point (x, y)

The potential function φ(x, y) itself is arbitrary, but it should monotonically decrease as we move away from the enemy position.

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The superposition property ：

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x

cx

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Shortest Path Algorithm BFS

When BFS terminates, every node knows its distance to the source and its parent point points to its parent along the path toward the source.

Every packet contains two fields How many hop it has traveled from the source The last node visited

Every node maintains a distance variable If a node receives multiple search packets from source, only pac

kets with smallest hop counts are forwarded. Proposition : In a network of n nodes, the number of to

tal packet transmissions required for the shortest path algorithm is O(n).

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Minimum Exposure Path Algorithm

When the algorithm terminates, every node knows the exposure of the minimum exposure path to the source.

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Greedy Perimeter Stateless Routing for Wireless Networks (GPSR) It is a greedy routing strategy for ad hoc networks

which utilizes geographic information to find its destination.

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Alternatives protocol : DSR, AODV DSR : Dynamic Source Routing AODV : Ad-Hoc On-Demand Distance Vector Rou

ting Do not utilize geographic information and instead

flood the network with query packets for finding routes.

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Perimeter routing - 1

Two paths : (xyzD) and (xwvD)

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Perimeter routing - 2

Traversing the cycle (xwvDzyx) by the right-hand rule amounts to navigating around the pictured void.

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Outlines

Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

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Navigation Using Uniform Skeleton Graph (USG)

Step 1: Construct a reduced graphEx: GPSR

Step 2: Carry out a search on the skeleton

graph to find shortest paths and minimal exposure paths

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Construct a reduced graph

Some node initiates the grid street construction protocol. Using GPSR.

Next we turn to the embedding of the perimeter street. Detect the danger zone boundary The node inside the danger zone can go to sleep The boundary node broadcast “wake up”

message with life time of w hop to its neighbor.

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grid streets : The grid streets are a square grid of lines separated by distance s from each other.

Perimeter streets : An additional set of streets which follow the perimeter of the danger zone is also included in the street map and they are the perimeter streets.

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.

.

.

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22Load balancing by shifting

How to avoid running out energy

This can be avoided by varying the value of s, the street separation; or by shifting all the streets by a constant amount in the diagonal direction.

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How to discover a path that points not on streets ?

What can one do for source and destination pairs which do not lie on any street?

If the destination does not lie on any street, then it is enclosed in a square enclosed by four streets.

Methods The destination can be found by flooding that limit

ed square. Construct the streets on-demand.

Automatic load balancing

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Navigation Using Uniform Skeleton Graph (USG)

Step 1: Construct a reduced graphEx: GPSR

Step 2: Carry out a search on the skeleton

graph to find shortest paths and minimal exposure paths

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The USG: basic properties

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＆b

a

L

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2D

3D

L

L

cD

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Outlines

Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

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Navigation Using Adaptive Skeleton Graph (ASG)

Idea of ASG Place streets densely near danger zones while sp

arsely far away from danger zones

How do they achieve that?Recursively divide the area into quadtree 四分樹 unt

il no quadtree cell whose boundary is intersected by danger zones boundary.

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Illustration of Constructing street map for ASG (Shortest Path)

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Illustration of Constructing street map for ASG (Minimum Exposure Path)

•The sensor at a danger point flood with BFS

•Every node finds it is equidistant from any two point declared as Voronoi edge

•Embeding street map on Voronoi edge using quadtree as before

The danger point : A,B,C

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Performance of ASG

ASG improves (compared to USG) not only the number of nodes

Implies lower communication cost but also the total path length

Implies performance boosting

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Theorem 4 : ASG basic property – 1 (minimum communication cost)

Communication cost of discovering the shortest path is nnO log2/1

The limits of communication cost

is

the limits of the size (length) of ASG

So we prove that the size of ASG is nnO log2/1

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pOOpO )1(

)(22/ pOOpO

# of node cross Perimeter

Length of the node

Total length of street at that level

)(44/ pOOpO )(88/ pOOpO

2/1nO

2/1nO

2/1nOp By definition of well-behaved curve

:

npO log Total length of street at all levels

Communication cost of ASG: )log(log 2/1 nnOnpO

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Theorem 5 : ASG basic property -2 (shortest path)

For a path joining any two points located on the streets in the adaptive skeleton graph

2/ OPTASG

lASG

lOPT

x

worst case

x/2

x/2

x222

x

x xx

OPT

ASG

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Theorem 6 : ASG basic property – 3(minimum exposure path)

For a path joint any two points located on the street in ASG

The proof is the same as corresponding Theorem for USG (Theorem 3), the size of square did not used in that proof, so

constS

S

OPT

ASG

constS

S

S

S

OPT

ASG

OPT

USG

SASG : the exposure for the adaptive skeleton graph.

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Performance Comparison USG with ASG

USG ASG

Communication Cost

Performance Radio of Shortest Path

Performance Radio of Minimum Exposure Path

2/1nO

cOPTUSG 12/

constSS OPTUSG / constSS OPTASG /

2/ OPTASG

nnO log2/1

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Outlines

Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

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Experimental Results Place n sensors in a area Do the experiment with n =1024, 4096 and 16384

nodes. Shortest path is tested with two types of danger zones

nn

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Experimental Results(Skeleton Graph Size v.s. Number of Nodes)

337 nodes~37%

659 nodes~4%

S : Simple

C : Complex

The uniform skeleton graph is slightly larger than the adaptive graph, but this difference is not highly significant.

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Experimental Results(Performance ratio for Shortest Path)

Performance Ratio = OPTASG /Generate 200 random point pairs lying within the sensor coverage area

The approximated path lengths are no worse than 50% of optimal,The adaptive skeleton graph performs better as expected.

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Experimental Results(Performance ratio for Minimum Exposure Path)

Use 20 different scenarios, each of which consists of three danger points

Compute 10 minimum exposure paths

Performance Ratio = OPTASG SS /

Both the uniform and adaptive skeleton graphs perform equally well with neither holding a decisive advantage.

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Conclusions

Shortest path and minimum exposure path can be solved using skeleton graph

The USG and ASG provide close to optimal paths with very low communication overhead

ASG is more scalable than USG

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References [8] Q. Li, M. DeRosa, and D. Rus, “Distributed algorithms for guid

ing navigation across a sensor network,” in Proc. of IPSN ’03., 2003.

[9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM 2000.

[14] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, “Exposure in wireless ad-hoc sensor networks,” in Proc. of MOBICOM 2001, 2001.

[15] G. Veltri, Q. Huang, G. Qu, and M. Potkonjak, “Minimal and maximal exposure path algorithms for wireless embedded sensor networks,” in Proc. of SenSys 2003, 2003.