Practical Virtual Coordinates for Large Wireless Sensor Networks - - PowerPoint PPT Presentation

Practical Virtual Coordinates for Large Wireless Sensor Networks

Jiangwei Zhou*, Yu Chen+, Ben Leong∇, Boqin Feng*

*Xi’an Jiaotong University

+ Duke University ∇ National University of Singapore

Practical Virtual Coordinates for Large Wireless Sensor Networks

Jiangwei Zhou*, Yu Chen+, Ben Leong∇, Boqin Feng*

*Xi’an Jiaotong University

+ Duke University ∇ National University of Singapore

Wireless Sensor Networks: Point-to-point routing is a useful primitive for data-centric applications

For small sensor networks (<200 nodes): pick your favorite algorithm.  SenSys 201 0

For large sensor networks (~3,200 nodes), geographic routing algorithms are most scalable:

• storage cost proportional to

network density not to size

• motes have small RAM

Problem

Geographic routing algorithms require coordinates!

Large networks ⇒ Big problem!

Wait A Moment… . Hasn’t the problem already been solved? Virtual Coordinates

[Rao et al., Mobicom 2003]

Related Work

• Virtual Coordinates

– NoGeo (Rao et al., Mobicom 2003) – GSpring (Leong et al., ICNP 2007) – GLoVE (Westphal et al., Infocom 2009)

• Look good in simulation
• Not practical or efficient for real

TinyOS motes

– 48 KB RAM – CC2420: 1 27-byte messages

Story of our failure

Tried to implement existing algorithms in TinyOS but failed!

Our Solution Particle Swarm Virtual Coordinates (PSVC)

Goal: Compute Euclidean Coordinates in a Scalable ble & & Distribu ibute ted Way

Overview

• 1. How PSVC works

– How we fix NoGeo (Rao et. al) – Why GSpring (Leong et al.) failed

• 2. How well PSVC works

– Performance – Cost

• 3. Current Limitations/Future Work

NoGeo (Rao et al., Mobicom’03)

reference node

elect reference node (maybe smallest id)

NoGeo (Rao et al., Mobicom’03)

reference node

NoGeo (Rao et al., Mobicom’03)

broadcast hop count

NoGeo (Rao et al., Mobicom’03)

elect p perimeter nodes

perimeter node

NoGeo (Rao et al., Mobicom’03)

perimeter nodes broadcast hop counts

NoGeo (Rao et al., Mobicom’03)

perimeter nodes broadcast hop counts

NoGeo (Rao et al., Mobicom’03)

perimeter nodes broadcast hop counts

Hop Counts→ Coordinates

Standard optimization problem (solved numerically)

             

− − 1 1 1 12 1 12 p p p p p p

h h h h h h      

∑∑

= =

− − =

p i p j ij j i

h x x E

1 1 2

) | (| min  

⇒

) , , , (

2 1 p

x x x    

p rows p columns

NoGeo (Rao et al., Mobicom’03)

Virtual Coordinate Space

NoGeo (Rao et al., Mobicom’03)

Project onto virtual circle

NoGeo (Rao et al., Mobicom’03)

Project onto virtual circle

NoGeo (Rao et al., Mobicom’03)

NoGeo (Rao et al., Mobicom’03)

Add remaining nodes

NoGeo (Rao et al., Mobicom’03)

Relaxation

, 1∑ =

k k i

x n x  

k is a

neighbor of i

NoGeo (Rao et al., Mobicom’03)

Relaxation

k is a

neighbor of i

, 1∑ =

k k i

x n x  

NoGeo (Rao et al., Mobicom’03)

Relaxation

k is a

neighbor of i

, 1∑ =

k k i

x n x  

NoGeo (Rao et al., Mobicom’03)

Relaxation

k is a

neighbor of i

, 1∑ =

k k i

x n x  

NoGeo (Rao et al., Mobicom’03)

Relaxation

k is a

neighbor of i

, 1∑ =

k k i

x n x  

NoGeo (Rao et al., Mobicom’03)

Convergence!

k is a

neighbor of i

, 1∑ =

k k i

x n x  

Issues with NoGeo

• Detect wrong perimeter nodes
• Too many perimeter nodes

–O(p2) broadcast messages

• Relaxation is slow
• Relaxation is not “stable”
• Limitation: 2D algorithm

(what about 3D networks?)

Summary

• Select reference node
• Elect perimeter nodes
• Initialization of perimeter nodes

– Error minimization – Project onto circle

• Relaxation

–average of neighbors

Summary

• Select reference node
• Elect perimeter nodes
• Initialization of perimeter nodes

– Error minimization – Project onto circle

• Relaxation

Key Insights

Summary

• Select reference node
• Too many perimeter nodes
• Initialization of perimeter nodes

– Error minimization – Project onto circle

• Relaxation

Key Insights

Summary

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization – Project onto circle

• Relaxation

Key Insights

Summary

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization using geometry – Project onto circle

• Relaxation

Key Insights

Summary

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization using geometry – Project onto circle

• Relaxation

Key Insights

Summary

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization using geometry – Project onto circle

• Spring Relaxation

Key Insights

What GSpring got Right

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization using geometry – Project onto circle

• Spring Relaxation

Key Insights

What GSpring got Right

• Select reference node
• Elect only 4 reference nodes
• Initialization of reference nodes

– Error minimization using geometry – Smarter Projection on circle

• Spring Relaxation

Key Insights

+ Extra

Particle Swarm Virtual Coordinates

reference node

The smalle allest node identifier(ID)

p1

maximum hops

Particle Swarm Virtual Coordinates

p1 p2

maximum hops

Particle Swarm Virtual Coordinates

p1 p2 p3

31

h

32

h

) max(

32 31

h h +

Particle Swarm Virtual Coordinates

p1 p2 p3 p4

41

h

42

h

43

h

) max(

43 42 41

h h h + +

Particle Swarm Virtual Coordinates

p1 p2 p4 p3

Each node knows of the hop counts between every pair of reference nodes

Particle Swarm Virtual Coordinates

p1 p2 p4 p3

Particle Swarm Virtual Coordinates

             

34 24 14 34 23 13 24 23 12 14 13 12

h h h h h h h h h h h h

Particle Swarm Virtual Coordinates

p1(0,0) p2(100h12,0)

Particle Swarm Virtual Coordinates

p1(0,0) p2(100h12,0) p3(x,y)

∑

− =

− − =

1 1 2

) 100 | (| min

k i ik j i

h x x E  

100h13 100h12

Particle Swarm Virtual Coordinates

∑

− =

− − =

1 1 2

) 100 | (| min

k i ik j i

h x x E  

p1(0,0) p2(100h12,0) p3(x,y) p4(x’,y’) 100h14 100h24 100h34

p1 p2 p4 p3

Each node knows its hop count to each reference node

Observation

Particle Swarm Virtual Coordinates

∑

=

− − =

4 1 2

) 100 | (| min

i ij j i j

h x p E  

p1(0,0) p2(100h12,0) p3(x,y) p4(x’,y’) xj

Particle Swarm Virtual Coordinates

Each node computes coordinates independently

Particle Swarm Virtual Coordinates

Each node computes coordinates independently

Particle Swarm Virtual Coordinates

Each node computes coordinates independently

Particle Swarm Virtual Coordinates

Each node computes coordinates independently

Particle Swarm Virtual Coordinates

Spring Relaxation

Spring Relaxation

• Spring force:

(Hooke’s Law)

• Net force:
• Update rule:

) ( |) | (

j i j i ij ij

x x u x x l F − × − − × = κ

∑

≠

=

i j ij i

F F

i i t i i i

F F F x x | | ) |, min(| α + =

THAT’S PSVC!!

Wait A Moment… .

Where’s the Particle Swarm?

Recall

∑

=

− − =

4 1 2

) 100 | (| min

i ij j i j

h x p E  

∑

− =

− − =

1 1 2

) 100 | (| min

k i ik j i

h x x E  

Particle Swarm Optimization: beam & local hill-climbing search (details in paper)

Key ideas

• 1. Need only a small number of

reference nodes ⇒ need to choose them well

• 2. Hop count good proxy for virtual

distance

• 3. Spring relaxation improves

convexity ⇒ increase greedy forwarding success rates

PERFO

ERFOMAN ANCE

EVALU

ALUATI ATION (TO (TOSSIM) M)

3, 3,200 200-node

• de Don
• nut Ne

ut Netw twork rk

Actual PSVC NoGeo

3, 3,200 200-node

• de Cros

Cross Ne Netw twork

• rk

Actual PSVC NoGeo

Gre Greedy f forw

• rwarding s

arding suc uccess rate rate v

• vs. ne

netw twork

• rk de

dens nsit ity

Performance: Hop Stretch (GDSTR) (3,200-node networks)

Network Type Physical coordinates NoGeo Sparse UDG (degree 1 0) 3% lower 1 0% lower Dense UDG (degree 1 6) Same 4% lower Obstacle (degree 8) 35% lower 35% lower

Can do better than actual coordinates!

3, 3,200 200-node

• de Ne

Network

• rk w

with ith Obs Obstacles es

Actual PSVC NoGeo

Coordinate assignment + Spring relaxation ⇒ increase convexity

Gre Greedy f forw

• rwarding

ng s suc uccess rate rate

• vs. I

Ite terat ations (for 3,

• r 3,200

200-node node 2D 2D ne netw twor

• rks)

relaxation unstable

NoGeo PSVC

Ove Overh rhead d pe per n r node

• de vs
• vs. Ne

Network

• rk size

ize

NoGeo PSVC Cost from propagation

• f reference

node hop counts

Limitations/Future Work

• PSVC fits in 48 KB TelosB

executable memory

• NoGeo, PSVC/GDSTR cannot fit
• Improve memory footprint
• Evaluation for incremental growth

and node failures

More details in paper

• PSO Algorithm
• Details of PSVC
• PSVC easily extensible to 3D
• Comparison of storage costs
• Two-hop greedy forwarding can

improve performance significantly

• Evaluations on 1 20-node Indriya

TelosB testbed

TinyOS Source Code

Available here: https://sites.google.com/site/geographicrouting

Conclusion

• Routing stretch

– Lower than NoGeo – Comparable to actual physical coordinates – Superior for networks with obstacles

• Converges fast (~1 0 iterations)
• Works for 3D networks (!)
• Practical : implemented in TinyOS and

evaluated in TelosB testbed

QUESTI

UESTIONS? S?

THANK YOU

Background

• Geographic routing is a promising approach

for wireless networks

– Achieve close to optimal routing stretch – Scale well – Routing states is dependent on local network density and not on network size

• Nodes need location information while no

location information is useful at hand

– Employ virtual coordinates

Case for Virtual Coordinates

• Not feasible to manually configure coordinates for

each node

• GPS does not work always
• Virtual coordinates are sometimes better, e.g.

sensornet on ship

• Actual physical locations are not required (Rao et al.,

2003)

• Previous work: good for dense networks and focused
• n 2D networks
• Know: greedy forwarding is efficient
• Challenge: can we assign coordinates so that greedy

forwarding always works even for 3D networks?

Related Work

• Routing algorithms based non-

Euclidean coordinate systems

– VPCR (Newsome et al., 2003) – BVR(Fonseca et al., 2005) – S4(Mao et al., 2007)

• Do not scale as well as geographic

routing for large (3,200 node) networks (SenSys 201 0)

GSpring (Leong et al., 2007)

reference node

GSpring (Leong et al., 2007)

p1

maximum hops

GSpring (Leong et al., 2007)

p1 p2

maximum hops

GSpring (Leong et al., 2007)

p1 p2 p3

1

h

2

h

GSpring (Leong et al., 2007)

p1 p2 p3 p4

1

h

2

h

3

h

GSpring (Leong et al., 2007)

p1 p2 p4 p3 p5 p6 p7 p8

Each will know of the hop counts between every pair of perimeter nodes

Projection onto Circle

p1 p2 p4 p3 p5 p6 p7 p8

Circumference = spring rest length x total hop count

Projection onto Circle

p1 p2 p4 p3 p5 p6 p7 p8 Arc proportional to hop count

Particle Swarm Virtual Coordinates (PSVC)

• Based on hop count
• Reference nodes are elected to compute

initial coordinates for all nodes

• Using PSO algorithm to minimize the

error when computing initial coordinates

• Running a iterative relaxation procedure

to make the virtual topology more convex

• PSVC can be trivially extended to 3D

coordinates

Determining Initial Coordinates

• Select reference nodes
• Initialization of reference nodes
• Coordinates for Non-reference nodes

Determining Initial Coordinates

• Select reference nodes
• Initialization of reference nodes
• Coordinates for Non-reference nodes

Initialization of reference nodes

p1 (0, 0,0) 0) p2 (100 100h12

12,0

,0) ) // hij is the hop count from pi to pj p3 (x3,y3) // x3 and y3 are computed with triangle equalities using 1 00h31 and 1 00h32, while error function is as

∑

− =

− − =

1 1 2

) 100 | (|

k i ik i k

h x x E

Determining Initial Coordinates

• Select reference nodes
• Initialization of reference nodes
• Coordinates for Non-reference nodes

Coordinates for Non-reference nodes

• Hop counts to all the reference nodes
• The coordinates of all the reference

nodes

• Use PSO to minimize the error of
• bjective function that maps the

assigned virtual coordinates for each node to their hop counts to the reference nodes

PSO equation and parameters

         − − = + = − + − + = ) ( ) ( ) (

min max max max 2 2 1 1

w w k k w w v x x x G r c x l r c v w v

i i i i i i i i i

, 8 . 1 , 100 , 1 . , 2 . 1 , 10

2 1 max min max

= = = = = = c c k w w POPSIZE

Parameters:

] 1 , [ , 2

1

∈ r r

Notes: To prevent floating point overflow, all inputs are normalized by dividing them by 1 00h12

Algorithm1 : Compute initial coordinates for non-reference nods with PSO

Given: Initialize for k=0 to kmax do for i=0 to POPSIZE do // where p is the number of the current node to the reference node j, is the position for reference node j. if then end if if then end if end for end for

p i pi , , 1 ,  =

POPSIZE i l v x

, , 1 , ], 1 , 1 [ ], 1 , 1 [  = = − ∈ − ∈

) (

w w k k w w − − =

∑ =

− − = + ← − + − + ←

h h p x error v x x x G r c x l r c v w v

) | (| ) ( ) (

p

Lerror error <

error Lerror x l

= ←

Gerror error <

error Gerror x G

= ←

∞ = = = ∞ = Gerror G POPSIZE i Lerror

, , , , 1 , 

Relaxation after initialization

• Spring force:

(Hooke’s Law)

• Net force:
• Update rule:

) ( |) | (

j i j i ij ij

x x u x x l F − × − − × = κ

∑

≠

=

i j ij i

F F

i i t i i i

F F F x x | | ) |, min(| α + =

Node joins after Convergence

• Listens to the stayalive beacons of its

neighbors to obtain their coordinates

• If all its neighbors have stabilized, it

computes its coordinates as a weighted sum of the coordinates of its neighbors’ coordinates

∑ ∑ ∑ ∑

= =

j j ij j ij i j j ij j ij i

y r r y x r r x 1 1

Performance

• Evaluation

– Testbed – TinyOS Simulator

• Measured metrics:

– Greedy forwarding success rate – Hop Stretch – Storage cost – Overhead

• Simulation topologies

– range of network densities (average node degree) – larger networks up to 3,200 nodes

• low/high density
• obstacles

Performance

• Routing algorithm: GDSTR
• Compare with

–actual coordinates –NoGeo (Rao et al., 2003)

Ave Averag age hop s hop stre tretch f h for GDS

• r GDSTR

agai against ne netw twor

• rk de

k dens nsity

Two wo-hop hop gre greedy for

• rwar

arding suc uccess rate rate agai against ne netw twor

• rk

k size ize in 2D ne in 2D netw twor

• rks

Ave Averag age hop s hop stre tretch h agai against ne netw twor

• rk

k size ize in 2D ne in 2D netw twor

• rks

Two wo-hop hop gre greedy for

• rwar

arding suc uccess rate rate agai against ne netw twor

• rk s

k size ize for 2D

• r 2D ne

netw twor

• rks w

with obs ith obstacles

Ave Averag age hop s hop stre tretch f h for GDS

• r GDSTR

agai against ne netw twor

• rk s

k size ize for 2D

• r 2D with obs

ith obstac acles

Maxim imum um s stora

• rage

ge c cost ve versus ne netw twor

• rk s

size ize f for 2d

• r 2d ne

netw twor

• rks

Messages s sent pe nt per r node node agai against ne netw twor

• rk

k size ize f for

• r 2D ne

2D netw twor

• rks

Two wo-hop hop gre greedy suc uccess rate rate agai against ne netw twor

• rk

k size ize f for

• r 3D ne

3D netw twor

• rks

Gre Greedy f forw

• rwarding

ng s suc uccess rate rate f for P

• r PSV

SVC C with ith 4, 4, 5, 5, 6 6 and 7 and 7 re referenc nce node nodes f for

• r 3D ne

3D netw twor

• rks

ks

Two wo-hop hop gre greedy for

• rwar

arding suc uccess rate rate for v vari rious

• us algo

gori rithm thms o

• n Indri

driya

Conclusion

• Converges faster and achieves a lower

hop stretch compared to NoGeo

• Scales well up to 3,200 nodes
• Makes no assumptions on the network

topology and can naturally be extended to three-dimensional(3D) wireless sensor networks