DRT: Decaying Bloom Filter Primer

1
Mobile Orthogonal Rendezvous Routing
Protocol (MORRP) Bow-Nan Cheng (RPI), Murat
Yuksel (UNR), Shivkumar Kalyanaraman (RPI)
DRT Details
DRT Inter-Node Decay

• Motivation
• Current RF-based ad hoc networks utilize
  omni-directional antennas, consume high power,
  are constrained by low bandwidth, and are highly
  error-prone. By contrast, free space optical
  (FSO) transceivers such as high-brightness LEDs
  (HBLEDs) are very low cost (2-5/transceiver
  package), highly reliable (10 year lifetime) and
  low power (100 microW for 10-100 Mbps), operate
  in license-free frequency bands, transmit at
  relatively higher bandwidth, and are more secure
  and spatially efficient due its transmissions
  directional nature.
• Hybrid FSO, THz FSO, and Directional RF
  techniques have high potential to scale high
  bandwidth wireless networks because the
  directional nature of transmissions utilizes the
  medium much more efficiently.
• In our work, we seek to investigate how to
  leverage directionality (which is standard on FSO
  and THz FSO links) to perform network routing in
  an unstructured, flat way in highly mobile
  environments.

MORRP Fields of Operation
1
4
B
Directional Routing Tables (DRT) map interface ID
to the probability of reaching a destination by
sending out that interface.
A
Z
C
D
2
3
Near Field Operation
Traditional Forwarding Tables (at A)
Directional Routing Table
Bitwise-OR
Far Field Operation
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1
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1
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1
1
1
Update DBF

Near Field Operation Uses Near Field DRT to
match for nodes 2-3 hops away Far Field
Operation RREQ / RREP much like ORRP except
nodes along path store info in Far-Field DRT
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Decayed DBF (drop 50 of Bits)
My ID (B)
A is now 100 sure B is 1 hop away while only 50
sure C can be reached through sending out
interface 1
Broadcasted by B to all Neighbors
h1(x), h2(x) hn(x)
via Decaying Bloom Filters
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ID ID
ID Set of IDs
Set of IDs Set of IDs
Performance Evaluation
DRT Decaying Bloom Filter Primer

• Metrics Evaluated
• Reachability Percentage of nodes reachable by
  each node in network (Hypothesis high
  reachability)
• Scalability The total state control packets
  flooding the network (Hypothesis higher than
  ORRP but lower than current protocols out there)
• Average Path Length
• End to End Delay (Latency)
• Aggregate Network Goodput
• Scenarios Evaluated
• Affect of Time Decay Factor on Reach for various
  mobility speeds
• Affect of Distance Decay Factor on Reach for
  various mobility speeds
• Affect of NF and FF Threshold on Reach for
  various mobility speeds
• Evaluation of metrics vs. AODV (reactive), OLSR
  (proactive), GPSR w/ GLS (position), ORRP under
  various node velocities, densities, and
  topology-sizes

Bloom Filter - A probabilistic algorithm to
quickly test membership in a large set using
multiple hash functions into a single array of
bits
Challenges
Traditional Bloom Filter Store Example
Traditional Bloom Filter Search Example
ID 1
ID 3
ID 1
ID 2
ID 1 4 bits found ID 1 IN set
ID 3 1 bit found ID 3 NOT IN set
Hash Functions
h1(x), h2(x) hn(x)
h1(x), h2(x) hn(x)

0
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1
1
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1
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1

1
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Traditional Bloom Filter Example To test whether
an ID is in the set, the ID is hashed through
each hash function (in example, there are 4 hash
functions) and if ALL positions in the bit array
corresponding to the hash are set to 1, then
the element is in the set.

• Coverage Issue
• Directional communications methods often need
  line of sight (LOS) or Near-LOS to transmit. How
  can we still provide high coverage even with
  directionality?

• 2. Mobility Issue
• Interface Handoff Reach not only depends on
  range but direction as well
• Field of View Nodes farther away incur
  seemingly less dynamism than nodes closer

NS2 Simulation Results

• Decaying Bloom Filter (DBF) Instead of having
  hard in set/not in set standards, the number of
  bits relative to the number of hash functions
  determines the percentage of certainty an element
  is in the set.
• Same example as above
• ID 1 4 bits match 100 certainty ID 1 is in
  set
• ID 3 1 bits match 25 certainty ID 3 is in
  set

MORRP Introduction
ORRP Summary

• ORRP Primitive
• Local sense of direction
• leads to ability to forward
• packets in opposite
• directions

A
1.2 Path Stretch

• High Connectivity (98)
• O(N3/2) State Complexity
• Low Path Stretch (1.2)
• High Goodput (30X vs. AODV and 10X vs. OLSR)
• Unstructured (Flat Topo)

98 Reach
A Directional Routing Table (DRT) is simply a
table that maps an interface ID / direction to a
decaying bloom filter that gives the of reach
of a specific node by sending out a specific
interface. Because
B
DBFs dictate certainty of reaching a node by
sending out an interface, the certainty must
change over time with node mobility
MORRP Extensions
A

• Conclusions
• MORRP achieves high reachability (93 -
  1300x1300m2 / 87 - 2000x2000m2) in high mobility
  (30m/s).
• MORRP shows that high reach can be achieved in
  probabilistic routing without the need to
  frequently disseminate node position information.
• MORRP yields over 13X the aggregate network
  throughput compared to AODV, OLSR, and GPSR w/
  GLS and 15 goodput increase compared to AODV and
  OLSR with 8 directional interfaces in highly
  mobile situations
• DRTs give a basic building block for using
  directionality to overcome issues with high
  mobility in MANET and DTNs
• This material is based upon work supported by the
  National Science Foundation under Grant Nos.
  IGERT 0333314, ITR 0313095, and STI 0230787. Any
  opinions, findings, and conclusions or
  recommendations expressed in this material are
  those of the author(s) and do not necessarily
  reflect the views of the National Science
  Foundation.

• Issue With mobility, straight line paths are
  hard to maintain (Reach drops to 60 w/ node
  vel. at 30m/s)
• What can we do?
• Replace intersection points with intersection
  regions
• Shift directions of send based on local node
  velocity
• Route packets probabilistically

DRT Intra-Node Decay
Time Decay w/ Mobility
Spread Decay with Mobility
A
a
1
x
2
B
As node moves in direction x, bits in DBF of
region 2 should decay faster than of region 1
depending on speed
As node moves in direction x, bits in DBF of
region 2 should be SPREAD to region 1 and 3
faster than the opposite direction
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Int ID 1
1
MORRP introduces a concept known as the
Directional Routing Table (DRT) to solve issues
caused by mobility
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Int ID 2
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Int ID 3