the impact of dht routing geometry on resilience and proximity
DESCRIPTION
The Impact of DHT Routing Geometry on Resilience and Proximity. New DHTs constantly proposed CAN, Chord, Pastry, Tapestry, Plaxton, Viceroy, Kademlia, Skipnet, Symphony, Koorde, Apocrypha, Land, ORDI … Each is extensively analyzed but in isolation - PowerPoint PPT PresentationTRANSCRIPT
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The Impact of DHT Routing Geometry on Resilience and Proximity
• New DHTs constantly proposed
– CAN, Chord, Pastry, Tapestry, Plaxton, Viceroy, Kademlia, Skipnet, Symphony, Koorde, Apocrypha, Land, ORDI …
• Each is extensively analyzed but in isolation
• Each DHT has many algorithmic details making it difficult to compare
Goals:a) Separate fundamental design choices from algorithmic detailsb) Understand their effect on reliability and efficiency
Source: The Impact of DHT Routing Geometry on Resilience and Proximity, K. Gummadi, et al.
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Approach: Component-based analysis
• Break DHT design into independent components
• Analyze impact of each component choice separately– compare with black-box analysis:
• benchmark each DHT implementation• rankings of existing DHTs vs. hints on better designs
• Two types of components– Routing-level : neighbor & route selection– System-level : caching, replication, querying policy etc.
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Outline
• Routing Geometry : A fundamental design choice
• Compare DHT Routing Geometries
• Geometry’s impact on Resilience
• Geometry’s impact on Proximity
• Discussion
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Three aspects of a DHT design
1) Geometry: a graph structure that inspires a DHT design, with its exciting properties
– Tree, Hypercube, Ring, Butterfly, Debruijn
2) Distance function: captures a geometric structure
– d(id1, id2) for any two node identifiers
3) Algorithm: rules for selecting neighbors and routes using the distance function
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Chord DHT has Ring Geometry
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Chord Distance function captures Ring
• Nodes are points on a clock-wise Ring
• d(id1, id2) = length of clock-wise arc between ids = (id2 – id1) mod N
d(100, 111) = 3
000
101
100
011
010
001
110
111
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Chord Neighbor and Route selection Algorithms
• Neighbor selection: ith neighbor at 2i distance
• Route selection: pick neighbor closest to destination
000
101
100
011
010
001
110
111 d(000, 001) = 1
d(000, 010) = 2
d(000, 001) = 4
110
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One Geometry, Many Algorithms
• Algorithm : exact rules for selecting neighbors, routes
– Chord, CAN, PRR, Tapestry, Pastry etc.
– inspired by geometric structures like Ring, Hyper-cube, Tree
• Geometry : an algorithm’s underlying structure
– Distance function is the formal representation of Geometry
– Chord, Symphony => Ring
– Many algorithms can have same geometry
Why is Geometry important?
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Insight:
Geometry Flexibility Performance
• Geometry captures flexibility in selecting algorithms
• Flexibility is important for routing performance
– Flexibility in selecting routes leads to shorter, reliable paths
– Flexibility in selecting neighbors leads to shorter paths
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Route selection flexibility allowed by Ring Geometry
• Chord algorithm picks neighbor closest to destination
• A different algorithm picks the best of alternate paths
000
101
100
011
010
001
110
111 110
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Neighbor selection flexibility allowed by Ring Geometry
• Chord algorithm picks ith neighbor at 2i distance
• A different algorithm picks ith neighbor from [2i , 2i+1)
000
101
100
011
010
001
110
111
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Outline
• Routing GeometryRouting Geometry
• Comparing flexibility of DHT Geometries
• Geometry’s impact on Resilience
• Geometry’s impact on Proximity
• Discussion
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Geometries we compare
Geometry Algorithm
Ring Chord, Symphony
Hypercube CAN
Tree Plaxton
Hybrid =
Tree + RingTapestry, Pastry
XOR
d(id1, id2) = id1 XOR id2Kademlia
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Metrics for flexibility
• FNS: Flexibility in Neighbor Selection= number of node choices for a neighbor
• FRS: Flexibility in Route Selection= avg. number of next-hop choices for all destinations
• Constraints for neighbors and routes
– select neighbors to have paths of O(logN)
– select routes so that each hop is closer to destination
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Flexibility in neighbor selection (FNS) for Tree
001000 011010 101100 111110
h = 2
h = 1
h = 3
• log N neighbors in sub-trees of varying heights
• FNS = 2i-1 for ith neighbor of a node
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Flexibility in route selection (FRS) for Hypercube
• Routing to next hop fixes one bit
• FRS =Avg. (#bits destination differs in)=logN/2
000
100
001
010
110 111
011
101
011d(000, 011) = 2 d(001, 011) = 1
d(010, 011) = 1
d(010, 011) = 3
FRS=avg. number of next-hop choices for all destinations
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Summary of our flexibility analysis
Flexibility Ordering of Geometries
Neighbors
(FNS)
Hypercube << Tree, XOR, Ring, Hybrid
(1) (2i-1)
Routes
(FRS)
Tree << XOR, Hybrid < Hypercube < Ring
(1) (logN/2) (logN/2) (logN)
How relevant is flexibility for DHT routing performance?
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Outline
• Routing GeometryRouting Geometry
• Comparing flexibility of DHT GeometriesComparing flexibility of DHT Geometries
• Geometry’s impact on Resilience
• Geometry’s impact on Proximity
• Discussion
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Analysis of Static Resilience
Two aspects of robust routing• Dynamic Recovery : how quickly routing state is recovered
after failures
• Static Resilience : how well the network routes before recovery finishes– captures how quickly recovery algorithms need to work
– depends on FRS
Evaluation:• Fail a fraction of nodes, without recovering any state
• Metric: % Paths Failed
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Does flexibility affect Static Resilience?
Tree << XOR ≈ Hybrid < Hypercube < Ring
Flexibility in Route Selection matters for Static Resilience
0
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0 10 20 30 40 50 60 70 80 90% Failed Nodes
% F
aile
d P
ath
s
Ring
Hybrid
XORTree
Hypercube
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Outline
• Routing GeometryRouting Geometry
• Comparing flexibility of DHT GeometriesComparing flexibility of DHT Geometries
• Geometry’s impact on ResilienceGeometry’s impact on Resilience
• Geometry’s impact on Proximity
– Overlay Path Latency
– Local Convergence (see paper)Local Convergence (see paper)
• Discussion
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Analysis of Overlay Path Latency
• Goal: Minimize end-to-end overlay path latency
– not just the number of hops
• Both FNS and FRS can reduce latency
– Tree has FNS, Hypercube has FRS, Ring & XOR have both
Evaluation:
• Using Internet latency distributions (see paper)
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0
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0 400 800 1200 1600 2000Latency (msec)
CD
F
FNS Ring
Plain Ring
FRS Ring
FNS + FRS Ring
Which is more effective, FNS or FRS?
Plain << FRS << FNS ≈ FNS+FRS
Neighbor Selection is much better than Route Selection
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0
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60
80
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0 400 800 1200 1600 2000Latency (msec)
CD
F
FNS Ring
FRS RingFNS XOR
FRS Hypercube
Does Geometry affect performance of FNS or FRS?
No, performance of FNS/FRS is independent of Geometry
A Geometry’s support for neighbor selection is crucial
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Summary of results
• FRS matters for Static Resilience – Ring has the best resilience
• Both FNS and FRS reduce Overlay Path Latency
• But, FNS is far more important than FRS– Ring, Hybrid, Tree and XOR have high FNS
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Limitations
• Not considered all Geometries
• Not considered other factors that might matter
– algorithmic details, symmetry in routing table entries
• Not considered all performance metrics
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Conclusions
• Routing Geometry is a fundamental design choice– Geometry determines flexibility
– Flexibility improves resilience and proximity
• Ring has the best flexibility– Good routing performance
Why not the Ring?