1. Department of Computer Science
Improving Search Efficiency Using Bloom Filters in Partially Connected Ad Hoc Networks: A Node-centric Analysis
Wing Ho Yuen
and
Henning Schulzrinne
Department of Computer Science
Columbia University

2. 7DS Application Motivation: Internet access is not ubiquitous
More Wi-Fi hotspots?
Ad hoc network to extend coverage of hotspots?
Node density insufficient to sustain connected networks
Instead of dropping packets, should store and forward in node and AP encounters
Goal
To emulate Internet services when users are disconnected such as delivery and web access

3. 3 Categories of 7DS Application
Download App
Subway map
download
Upload App
delivery
P2P App
music
exchanges

4. Data Retrieval Problem
Push-based
Data holder (DH) acts as server
Data querier (DQ) acts as client
Push-based
Small query overhead
Summary overhead
Pull-based (Query-based)
Large query overhead
summary
data
query DH DQ
Pull-based
data
query DH DQ

5. Bloom Filter Used in supporting membership queries Data Structure
DH transmits a Bloom filter
DQ queries an object only if a match occurs
Data Structure
Bloom filter consists of a binary m-bit vector
DH has n data objects x1,…,xn
Each object hashed by k independent hash functions h1,…,hk with range{0,1,2…,m-1}
if h(x1)=a, set BF[a]=1

6. Bloom Filter Example Bloom filter length (m=12) # hash functions (k=3)
Data Holder has {x1,x2},
Data Querier wants y1,x2,y2
Testing with Bloom filter
y1 not available
x2 is available
(false negative not possible)
Y2 is available
(false positive possible) x2 x1 1 x2 y1 1 y2

7. Single Neighbor Scenario
One DH; one DQ
Utilization
Fraction of time used for data transmission
measures inefficiency due to query overhead and Bloom Filter overhead
Assuming query success probability  is constant
Result
E[Z]: mean data Tx time E[Y]: mean query Tx time DQ DH

8. - Utilization E[T] E[T] BF length E[T] #hash fcns
E[T]: expected connection time
Small # hash functions, small complexity
High utilization
Small Bloom filter overhead
E[T]

9. Multiple Neighbors ScenarioDH DH
Querying is more effective
More DHs to answer a query
Multiple Bloom filter transmissions in a single busy period of an observer node
Node-centric model DQ DH DH DQ DH DQ BF BF BF BF DH BF BF BF BF BF DQ DH BF BF BF DQ DQ

10. Search Efficiency K=0 K=1 K=2 BF BF BF BF B I 1 cycle Timeline
Fraction of effective busy time  fraction of green colored blocks over 1 cycle
utilization gives the fraction of data transmission time in the green colored blocks
K=0
K=1
K=2 BF BF BF BF B I
1 cycle

11. Queueing Formulation
Observer node is a server, providing service to every node in range
Arrival occurs when a node enters observer range
N(t) neighbors receives service at time t
Modeled by M/M/∞ queue
n neighbors, departure rate is n
N(t) is the system state
=/ is the average number of nodes seen by observer 1 2 3 4 5 6   3 2 5 4 6 7

12. Bloom Filter Based Scheme
TBF
Data+Query
Binit
Bsub,1
Bsub,2
Bsub,K tK
tK+1 t0 t1 t2 t3
Sub-busy period begins at random N(tk), e.g. N(t1)=3
Busy period ends at tK+1 when N(tk+1)=0

13. Efficiency vs. 
Low bandwidth scenario
High bandwidth scenario

14. Conclusion Push is better than pull
Suitable for web access where query success probability is small
Node-centric model is more versatile than location-centric model
Realistic mobility model
Both node encounters and residence time can be measured online
Realistic interference model
Poisson field of interferers rather than collocated nodes