Efficient Hop ID based Routing for Sparse Ad Hoc Networks
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Transcript of Efficient Hop ID based Routing for Sparse Ad Hoc Networks
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Efficient Hop ID based Routing for Sparse Ad Hoc Networks
Yao Zhao1, Bo Li2, Qian Zhang2,
Yan Chen1, Wenwu Zhu31 Lab for Internet & Security Technology, Northwestern University2 Hong Kong University of Science and Technology3 Microsoft Research Asia
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Outline
• Motivation• Hop ID and Distance Function• Dealing with Dead Ends• Evaluation• Conclusion
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Dead End Problem
• Geographic distance dg fails to reflect hop distance dh (shortest path length)
E DS
A
),(),( DEdDAd hh
),(),( DAdDEd gg
But
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Fabian Kun, Roger Wattenhofer and Aaron Zollinger, Mobihoc 2003
GFG/GPSR
GOAFR+
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Network Density [nodes per unit disk]
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Greedy success
Connectivity
Geographic routing suffers from dead end problem in sparse networks
Motivation
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Related Work to Dead End Problem
• Fix dead end problem– Improves face routing: GPSR, GOAFR+, GPVF
R– Much longer routing path than shortest path
• Reduce dead ends“Geographic routing without location inform
ation” [Rao et al, mobicom03] – Works well in dense networks– Outperforms geographic coordinates if obstacle
s or voids exist– Virtual coordinates are promising in reducing de
ad ends– However, degrades fast as network becomes sp
arser
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• Motivation• Hop ID and Distance Function• Dealing with Dead Ends• Evaluation• Conclusion
Outline
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Virtual Coordinates
• Problem definition– Define and build the virtual
coordinates, and– Define the distance function based
on the virtual coordinates– Goal: routing based on the virtual
coordinates has few dead ends even in critical sparse networks • virtual distance reflects real distance• dv ≈ c · dh , c is a constant
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What’s Hop ID• Hop distances of a node to all the
landmarks are combined into a vector, i.e. the node’s Hop ID.
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A
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Lower and Upper Bounds
• Hop ID of A is• Hop ID of B is
),,,( )1()1(2
)1(1 mHHH
),,,( )2()2(2
)2(1 mHHH
),(),(),( BAdLBdLAd hihih
),(|),(),(| BAdLBdLAd hihih
UHHMindHHMaxL kkkhkkk )(|)(| )2()1()2()1(
A
B
Li
• Triangulation inequality
(1)
(2)
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How Tight Are The Bounds?• Theorem [FOCS'04)]
– Given a certain number (m) of landmarks, with high probability, for most nodes pairs, L and U can give a tight bound of hop distance • m doesn’t depend on N, number of
nodes – Example: If there are m landmarks, with
high probability, for 90% of node pairs, we have U≤1.1L
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Lower Bound Better Than Upper Bound
• One example: 3200 nodes, density λ=3π• Lower bound is much closer to hop distance
LU
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Lower bound vs Upper bound
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Lower Bound Still Not The Best
• H(S) = 2 1 5• H(A) = 2 2 4• H(D) = 5 4 3• L(S, D) = L(A, D) = 3• |H(S) – H(D)|= 3 3 2• |H(A) – H(D)|= 3 2 1 22
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S DA
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Other Distance Functions• Make use of the whole Hop ID vector
• If p = ∞, • If p = 1,
• If p = 2,
• What values of p should be used?
pm
k
pkkp HHD
1
)2()1( ||
m
kkkp HHD
1
)2()1( ||
m
kkkp HHD
1
2)2()1( ||
LDp
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The Practical Distance Function• The distance function d should be able
to reflect the hop distance dh
– d ≈ c · dh , c is a constant– L is quite close to dh (c = 1)
• If p = 1 or 2, Dp deviates from L severely and arbitrarily
• When p is large, Dp ≈ L ≈ dh– p = 10, as we choose in simulations
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Power Distance Better Than Lower Bound
LDp
00.10.20.30.40.50.6
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cent
agePower distance vs Lower bound
LDp
Difference to Hop Distance
[0,1) [1,2) [2,3)[3, 4) [4,5) ≥5
• 3200 nodes, density λ=3π
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Outline
• Motivation• Hop ID and Distance Function• Dealing with Dead Ends• Evaluation• Conclusion
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Dealing with Dead End Problem• With accurate distance function based
on Hop ID, dead ends are less, but still exist
• Landmark-guided algorithm to mitigate dead end problem– Send packet to the closest landmark to
the destination– Limit the hops in this detour mode
• Expending ring as the last solution
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Example of Landmark Guided Algorithm
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DDp(L2, D)>Dp(S,D)Dead End
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Detour
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Greedy
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Dp(S, D)>Dp(A, D)
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Practical Issues
• Landmark selection– O(m·N) where m is the number of landm
arks and N is the number of nodes• Hop ID adjustment
– Mobile scenarios– Integrate Hop ID adjustment process int
o HELLO message (no extra overhead)• Location server
– Can work with existing LSes such as CARD, or
– Landmarks act as location servers
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Outline
• Motivation• Hop ID and Distance Function• Dealing with Dead Ends• Evaluation• Conclusion
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Evaluation Methodology • Simulation model
– Ns2, not scalable– A scalable packet level simulator
• No MAC details• Scale to 51,200 nodes
• Baseline experiment design– N nodes distribute randomly in a 2D square– Unit disk model: identical transmission range
• Evaluation metrics– Routing success ratio– Shortest path stretch– Flooding range
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Evaluation Scenarios• Landmark sensitivity• Density• Scalability• Mobility• Losses• Obstacles• 3-D space• Irregular shape and voids
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Simulated Protocols• HIR-G: Greedy only• HIR-D: Greedy + Detour• HIR-E: Greedy + Detour + Expending ring• GFR: Greedy geographic routing • GWL: Geographic routing without location
information [Mobicom03]• GOAFR+: Greedy Other Adaptive Face
Routing [Mobihoc03]
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Number of Landmarks
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HIR-G λ=3πHIR-D λ=3πHIR-G λ=2πHIR-D λ=2π
Number of Landmarks• 3200 nodes, density shows average number of
neighbors• Performance improves slowly after certain value
(20)• Select 30 landmarks in simulations
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Number of Landmarks
Floo
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λ=3πλ=2π
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Density• HIR-D keeps high routing success ratio even in
the scenarios with critical sparse density.• Shortest path stretch of HIR-G & HIR-D is close
to 1.
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HIR-GHIR-DHIR-EGFRGOAFR+GWL
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Scalability
• HIR-D degrades slowly as network becomes larger• HIR-D is not sensitive to number of landmarks
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Conclusions
• Hop ID distance accurately reflects the hop distance and
• Hop ID base routing performs very well in sparse networks and solves the dead end problem
• Overhead of building and maintaining Hop ID coordinates is low
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Thank You!
Questions?
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Lower Bound vs Upper Bound• Lower bound is much close to hop distance
LU
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Per
cent
ageLower bound vs Upper bound
LU
Difference to Hop Distance
0 1 23 4 >4
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• If two nodes are very close and no landmarks are close to these two nodes or the shortest path between the two nodes, U is prone to be an inaccurate estimation
• U(A, B) = 5, while dh(A, B)=2
U Is Not Suitable for Routing
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Landmark Selection
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Hop ID Adjustment• Mobility changes topology• Reflooding costs too much overhead• Adopt the idea of distance vector
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13 Neighbor
s{23, 13}
Neighbors
{23}
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Build Hop ID System• Build a shortest path tree• Aggregate landmark candidates• Inform landmarks• Build Hop ID
– Landmarks flood to the whole network.• Overall cost
– O(m*n), m = number of LMs, n=number of nodes
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Mobility
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Pause time(s)
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HIR-G(λ=3π)HIR-D(λ=3π)HIR-G(λ=5π)HIR-D(λ=5π)
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GFG/GPSR
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Network Density [nodes per unit disk]
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• Geographic routing suffers from dead end problem in sparse networks• Fabian Kun, Roger Wattenhofer and Aaron Zollinger, Mobihoc 2003
Motivation
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Sho
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Greedy success
Connectivity
critical
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Virtual Coordinates
• Problem definition– Define the virtual coordinates
• Select landmarks• Nodes measure the distance to landmarks• Nodes obtain virtual coordinates
– Define the distance function– Goal: virtual distance reflects real
distance– dv ≈ c · dh , c is a constant