On Complex Enumeration for Multiuser MIMO Vector Precoding
Ad Hoc Now2008 Probabilistic Query Dissemination
1. Zinaida Benenson Felix Freiling
Markus Bestehorn Marek Jawurek
Query Dissemination with Predictable
Erik Buchmann
Query Dissemination with Predictable
Reachability and Energy Usage in Sensor
Networks
AdHoc-Now 2008, Sophia Antipolis
www.kit.edu
2. Introduction – Sensor Networks
A sensor network consists multiple of sensor nodes, e.g.Introduction
Problem Desc.
IdIdea
Reachability
Direct
I di t
MicaZ
Sun SPOT
Indirect
Topology
Information
Sensor Nodes
Battery-powered
Equipped with sensor hardware
Evaluation
Setup
Simulation
Break Even Equipped with sensor hardware
Limited computing resources
Wireless communication
Break-Even
Deployment
Conclusion
Q&A
Slide 2Markus Bestehorn
3. Query Processing in WSN
Generic query processing in sensor networks approach:
1. Disseminate query through base station
Introduction
Problem Desc.
Id
q y g
SELECT MAX(temp) FROM sensors …
2. Measure data using sensing hardware
3 Process & route query results back to base station
Idea
Reachability
Direct
I di t 3. Process & route query results back to base station
Optimization Goal: Reduce energy consumption!
Indirect
Topology
Information
Sending/Receiving data most expensive!
2
15°C
17°C
Evaluation
Setup
Simulation
Break Even 2
3
4
6
17°C
21°C
QQQ
Q
QQ
Break-Even
Deployment
Conclusion
3
1
5 Basestation
20°C
19°C
22°C
QQQ
Q
22°CQ&A
Slide 3Markus Bestehorn
4. Challenges for Query Dissemination
Unnecessary rebroadcasts must be avoided
Nodes should receive query only once
Introduction
Problem Desc.
Id
q y y
Idea
Reachability
Direct
I di t
2 4 6
Q Q
?
Existing approaches
Indirect
Topology
Information
31
5Q
Q
Existing approaches
Topology-Based: Determine rebroadcasting nodes using
accurate local topology information
Evaluation
Setup
Simulation
Break Even 2-Hop topology information is very costly
Optimal Broadcast Dominating Set Problem NP-complete
Probabilistic: Nodes rebroadcast with probability p
Break-Even
Deployment
Conclusion
High p high energy consumption
Low p not all nodes reached
How to set p?
Q&A
Slide 4Markus Bestehorn
5. Idea & Agenda
General idea:
Acquire basic topology information
Introduction
Problem Desc.
Id
q p gy
does not consume as much energy
Use probabilistic approach to disseminate query
Set rebroadcast probability based on basic topology information
Idea
Reachability
Direct
I di t Set rebroadcast probability based on basic topology information
Agenda:
Indirect
Topology
Information
Prediction framework
How to predict reachability for a given rebroadcast probability p?
How to set p based on prediction to reach all nodes?
Evaluation
Setup
Simulation
Break Even How to set p based on prediction to reach all nodes?
Topology Discovery
Possibilities to aquire required topology information?
Extensive evaluation
Break-Even
Deployment
Conclusion
Extensive evaluation
Simulation and real deployment results
Explore tradeoff reachability vs. energy consumption
A f th P di ti F k?
Q&A
Slide 5Markus Bestehorn
Accuracy of the Prediction Framework?
6. Hop Set Modell (1)
Task: Predict the number of reached nodes given
Topology information
Introduction
Problem Desc.
Id
p gy
Rebroadcast probability p
Hop Set: Hop Set H[i] contains all nodes that can be
reached by the base station via i hops
Idea
Reachability
Direct
I di t reached by the base station via i hopsIndirect
Topology
Information
H[1]H[2]H[3] H[0]
Evaluation
Setup
Simulation
Break Even
2 4 6
Break-Even
Deployment
Conclusion
31 5
Q&A
Slide 6Markus Bestehorn
7. Hop Set Modell (2)
Possibilities to reach a node via broadcast
Direct: Message is sent from node in H[i-1] to node in H[i]
Introduction
Problem Desc.
Id
g [ ] [ ]
Indirect: Message is sent from node in H[i] to node in H[i]
Backwards: Node in H[j] with j > i forwards message to node in
H[i] Simplification: not considered
Idea
Reachability
Direct
I di t H[i] Simplification: not consideredIndirect
Topology
Information
Evaluation
Setup
Simulation
Break Even 4
H[1]H[2]H[3] H[0]
QQQBreak-Even
Deployment
Conclusion
2
4
6
Q
Q
Q
Q
Q
Q&A 31 5
Slide 7Markus Bestehorn
8. Reachability Prediction
R(h,p) := number of reached nodes in Hop Set h with
rebroadcast probability p
Introduction
Problem Desc.
Id
p y p
R(0,p) = 1 base station is always „reached“
R(1,p) = |H[1]|
base station always broadcasts H[1]
Idea
Reachability
Direct
I di t base station always broadcasts
Hop Set H[1] always reached
Nodes in s bseq ent Hop Sets are reached
H[1]Indirect
Topology
Information
Nodes in subsequent Hop Sets are reached
Directly Direct(h,p)
Example: Direct(2,p)=4
Indirectly Indirect(h p) H[1]
Evaluation
Setup
Simulation
Break Even Indirectly Indirect(h,p)
Example: Indirect(2,p)=2
H[1]
H[2]
Break-Even
Deployment
Conclusion
R(h,p) := Direct(h,p) + Indirect(h,p) with h > 1Q&A
Slide 8Markus Bestehorn
9. Direct Reachability Prediction
Basic Idea to compute Direct(h,p)
Possible rebroadcasters |H[h-1]| nodes
H[i]H[i-1]Introduction
Problem Desc.
Id
| [ ]|
Potential Rebroadcasters R(h-1,p) nodes
Rebroadcasters R(h-1,p)·p nodes
|H[h-1]|
R(h 1 )
Idea
Reachability
Direct
I di t
|H[h 1]|
R(h-1,p)
R(h-1,p) ·p
Indirect
Topology
Information
P(„Node in H[h] directly reached“) can be computed
Evaluation
Setup
Simulation
Break Even
Avg. Number of connections from
H[i] to H[i-1] Connectivity[h]
Detailed description in the paper
Break-Even
Deployment
Conclusion
p p p
Direct(h,p) = P(reached directly)·s[h]
p
Rebroadcast
Probability
H[i]
Nodes reached
in i Hops
Q&A
Slide 9Markus Bestehorn
p
10. Indirect Rechability Prediction
Idea to compute Indirect(h,p):
Potential Rebroadcasters Direct(h,p)
Introduction
Problem Desc.
Id
( ,p)
Rebroadcasters Direct(h,p)·p
Average Number of connections within a Hop set
Interconnectivity[h]
Idea
Reachability
Direct
I di t Interconnectivity[h]
Indirect(h,p)=Direct(h,p)·p·Interconnectivity[h]
Indirect
Topology
Information H[1]H[2] H[0]
Evaluation
Setup
Simulation
Break Even
4 6
Implicit Assumption:
Break-Even
Deployment
Conclusion
3 5
Implicit Assumption:
Reached nodes distributed
evenly within hop sets
Q&A p
Rebroadcast
Probability
H[i]
Nodes reached
in i Hops
Slide 10Markus Bestehorn
p
11. Reachability Prediction (3)
R(h,p) computes reached nodes in Hop Set h with
rebroadcast probability p
Introduction
Problem Desc.
Id
p y p
Computing total reachability for given p:
( )( )][min)( hHphRpR ∑=
Idea
Reachability
Direct
I di t
Minimum required because Direct(h p) + Indirect(h p) > H[h]
( )( )][,,min)( hHphRpR
h
∑=Indirect
Topology
Information
Minimum required because Direct(h,p) + Indirect(h,p) > H[h]
possibleEvaluation
Setup
Simulation
Break Even
Also available:
Number of sent messages / rebroadcasting nodes
Break-Even
Deployment
Conclusion
Number of sent messages / rebroadcasting nodes
Number of received messages
Allows estimation of energy consumption!
Q&A
Slide 11Markus Bestehorn
12. Topology Information
Required Topology Information for Reachability Prediction
Set Size: Number of Nodes in each Hop Set H[h]
Introduction
Problem Desc.
Id
p [ ]
Connectivity: Avg. Number of connections a node in H[h] has
to nodes in H[h-1]
Interconnectivity: Avg Number of connections a node in H[h]
Idea
Reachability
Direct
I di t Interconnectivity: Avg. Number of connections a node in H[h]
has to other nodes in H[h]
Example:
Indirect
Topology
Information
H[i]H[i-1] Set size Connectivity
Evaluation
Setup
Simulation
Break Even
… i-1 i …
… 2 3 …
… i-1 i …
… 1.5 2 …
I t ti it
Break-Even
Deployment
Conclusion
Interconnectivity
… i-1 i …
… 0 4/3 …
Q&A
Slide 12Markus Bestehorn
… 0 4/3 …
13. Acquiring Topology Information
Several options to get required topology information:
Echo Algorithm
Introduction
Problem Desc.
Id
g
Expansion Wave: Explore network by initiating a flooding at the
base station
Contraction Wave: Aggregate topology information towards base
Idea
Reachability
Direct
I di t
gg g p gy
station
Drawback: Energy consumption, Scalability
Gossiping: Nodes attach routing information to messages
Indirect
Topology
Information
Gossiping: Nodes attach routing information to messages
Advantage: No extra messages
Drawback: Routing information disperses slowly
Routing Protocol Extraction: Extract topology information
Evaluation
Setup
Simulation
Break Even Routing Protocol Extraction: Extract topology information
from data structures of routing protocol
Drawback: Only possible for some protocols (AODV)
N t
Break-Even
Deployment
Conclusion
Note:
Even for Echo Algorithm Prediction pays off after a few
query disseminations!
Q&A
Slide 13Markus Bestehorn
q y
14. Evaluation - Setup
Network: 125 to 425 nodes
Node Degree: 4 – 16
Introduction
Problem Desc.
Id
g
Different Topology Types used, e.g.
Uniform: Nodes are placed uniformly around basestation
G i G i di ib i f d d b i
Idea
Reachability
Direct
I di t Gaussian: Gaussian distribution of nodes around basestation
100 topologies per topology type, 40 queries per topology
Energy prediction based values measured on MicaZ
Indirect
Topology
Information
Energy prediction based values measured on MicaZ
Criteria for success:
Evaluation
Setup
Simulation
Break Even
Accurate Prediction for Reachability and Energy
Optimization of probabilistic rebroadcast parameter p
to reach ALL nodes with query
Break-Even
Deployment
Conclusion
to reach ALL nodes with query
without rebroadcasting at each node
Exploration of rebroadcast probability – reachability tradeoff
Q&A
Slide 14Markus Bestehorn
15. Evaluation – Simulation Results
Result for node degree 16, 425 nodesIntroduction
Problem Desc.
Id
Uniform Gaussian
Idea
Reachability
Direct
I di t
p0
Indirect
Topology
Information
Evaluation
Setup
Simulation
Break Even
Findings:
Break-Even
Deployment
Conclusion
Reachability & energy prediction accurate
For most experiments, there exists a p0<1: Increasing p beyond
p0 does not pay off regarding reachability!
Q&A
Slide 15Markus Bestehorn
p0 p y g g y
energy savings without reducing reachability
16. Break Even Point
Exemplary computation:
Uniform topology
Introduction
Problem Desc.
Id
p gy
425 nodes, node degree 16
Assuming
T l di i h E h Al i h
Idea
Reachability
Direct
I di t Topology discovery using the Echo Algorithm
Energy consumption values measured on MicaZ
Indirect
Topology
Information
Topology Discovery consumes 722 mAs
Query dissemination with simple flooding (p=1) consumes
370 A
Evaluation
Setup
Simulation
Break Even 370 mAs
Using prediction framework for 99% reachability
p=0.6 220 mAs
Break-Even
Deployment
Conclusion
p
Result:
Topology Discovery pays off after 5 queries!
Q&A
Slide 16Markus Bestehorn
17. Evaluation – SPOT Deployment
17 SPOTs + Basestation deployed
10 Queries were disseminated into the
Introduction
Problem Desc.
Id 10 Queries were disseminated into the
network using
Simple flooding (p=1)
P b bili ti fl di
Idea
Reachability
Direct
I di t Probabilistic flooding
Prediction algorithm was used to reach
All nodes
Indirect
Topology
Information
At lowest possible rebroadcast prob. p
Result:
Broadcast Reached Sent Msg Received
Evaluation
Setup
Simulation
Break Even Broadcast
Algorithm
Reached
Nodes
Sent Msg. Received
Msg.
Simple 16.3 16.3 63.8
Probabilistic 15 4 10 2 34
Break-Even
Deployment
Conclusion
Probabilistic Rebroadcast Optimization
~30% less sent messages
Probabilistic 15.4 10.2 34
Q&A
Slide 17Markus Bestehorn
almost 50% less received messages
18. Summary
Explored relations between
Reachability
Introduction
Problem Desc.
Id
y
Energy consumption for query dissemination
Energy spent to acquire topology information
I t d d l ti l f k
Idea
Reachability
Direct
I di t Introduced analytical framework
Determines p0<1 for probabilistic broadcasting to reach all
nodes
Indirect
Topology
Information
Allows predictions regarding
sent / received messages
Energy consumption
Evaluation
Setup
Simulation
Break Even
gy p
Energy spent for topology information pays off after a few (5)
query disseminations
Even if echo algorithm is used!
Break-Even
Deployment
Conclusion
Even if echo algorithm is used!
Evaluation using Simulation & real Sensor network
Q&A
Slide 18Markus Bestehorn
19. Outlook
Integrate „backwards“ reachability into
framework
Introduction
Problem Desc.
Id
More topology information required?
Payoff?
Relation between query dissemination and query result
Idea
Reachability
Direct
I di t Relation between query dissemination and query result
accuracy
Indirect
Topology
Information
p0
~100% reachability
100% accuracy
~100% reachability
100% accuracy
<100% reachability
? accuracy
<100% reachability
? accuracy
Evaluation
Setup
Simulation
Break Even
Dynamic usage of different broadcast algorithms
Probabilistic approach good for dense networks
Break-Even
Deployment
Conclusion
Probabilistic approach good for dense networks
Switch to other broadcast algorithms in less populated areas of
the network?
Q&A
Slide 19Markus Bestehorn
20. Thank you for your attention!
Introduction
Problem Desc.
Id
Questions?
Idea
Reachability
Direct
I di tIndirect
Topology
Information
Evaluation
Setup
Simulation
Break EvenBreak-Even
Deployment
Conclusion
Q&A
Slide 20Markus Bestehorn