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The Impact of DHT Routing Geometry on Resilience and Proximity. Krishna Gummadi, Ramakrishna Gummadi, Sylvia Ratnasamy, Steve Gribble, Scott Shenker, Ion Stoica. Distributed Hash Tables (DHTs). DHTs are structured overlays that offer extreme scalability hash-table-like lookup interface

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the impact of dht routing geometry on resilience and proximity

The Impact of DHT Routing Geometry on Resilience and Proximity

Krishna Gummadi, Ramakrishna Gummadi,

Sylvia Ratnasamy,

Steve Gribble, Scott Shenker, Ion Stoica

distributed hash tables dhts
Distributed Hash Tables (DHTs)
  • DHTs are structured overlays that offer
    • extreme scalability
    • hash-table-like lookup interface
  • Ideal substrate for many distributed applications
    • file-systems, storage, backups, event-notification, e-mail, chat, databases, sensor networks ...
  • Applications need reliable and efficient DHT routing
motivation
Motivation
  • 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:

  • Separate fundamental design choices from algorithmic details
  • Understand their affect reliability and efficiency
our approach component based analysis
Our 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.
outline
Outline
  • Routing Geometry: A fundamental design choice
  • Compare DHT Routing Geometries
  • Geometry’s impact on Resilience
  • Geometry’s impact on Proximity
  • Discussion
three aspects of a dht design
Three aspects of a DHT design
  • Geometry: a graph structure that inspires a DHT design, with its exciting properties
    • Tree, Hypercube, Ring, Butterfly, Debruijn
  • Distance function: captures a geometric structure
    • d(id1, id2) for any two node identifiers
  • Algorithm: rules for selecting neighbors and routes using the distance function
chord distance function captures ring

d(100, 111) = 3

Chord Distance function captures Ring

000

111

001

  • Nodes are points on a clock-wise Ring
  • d(id1, id2) = length of clock-wise arc between ids

= (id2 – id1) mod N

110

010

101

011

100

chord neighbor and route selection algorithms
Chord Neighbor and Route selection Algorithms

000

110

111

d(000, 001) = 1

001

  • Neighbor selection: ith neighbor at 2idistance
  • Route selection: pick neighbor closest to destination

110

010

d(000, 010) = 2

101

011

100

d(000, 001) = 4

one geometry many algorithms
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?

insight geometry flexibility performance
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
route selection flexibility allowed by ring geometry
Route selection flexibility allowed by Ring Geometry

000

110

111

001

  • Chord algorithm picks neighbor closest to destination
  • A different algorithm picks the best of alternate paths

110

010

101

011

100

neighbor selection flexibility allowed by ring geometry
Neighbor selection flexibility allowed by Ring Geometry

000

111

001

  • Chord algorithm picks ith neighbor at 2idistance
  • A different algorithm picks ith neighbor from [2i , 2i+1)

110

010

101

011

100

outline1
Outline
  • Routing Geometry
  • Comparing flexibility of DHT Geometries
  • Geometry’s impact on Resilience
  • Geometry’s impact on Proximity
  • Discussion
metrics for flexibilities
Metrics for flexibilities
  • 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
flexibility in neighbor selection fns for tree
logN neighbors in sub-trees of varying heights

FNS = 2i-1for ithneighbor of a node

Flexibility in neighbor selection (FNS) for Tree

h = 3

h = 2

h = 1

000

001

010

011

100

101

110

111

flexibility in route selection frs for hypercube
Flexibility in route selection (FRS) for Hypercube

110

111

  • Routing to next hop fixes one bit
  • FRS =Avg. (#bits destination differs in)=logN/2

d(010, 011) = 3

100

101

010

011

d(010, 011) = 1

000

001

011

d(000, 011) = 2

d(001, 011) = 1

summary of our flexibility analysis
Summary of our flexibility analysis

How relevant is flexibility for DHT routing performance?

outline2
Outline
  • Routing Geometry
  • Comparing flexibility of DHT Geometries
  • Geometry’s impact on Resilience
  • Geometry’s impact on Proximity
  • Discussion
analysis of static resilience
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 routesbefore 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
does flexibility affect static resilience
Does flexibility affect Static Resilience?

Tree << XOR ≈ Hybrid < Hypercube < Ring

Flexibility in Route Selection matters for Static Resilience

outline3
Outline
  • Routing Geometry
  • Comparing flexibility of DHT Geometries
  • Geometry’s impact on Resilience
  • Geometry’s impact on Proximity
    • Overlay Path Latency
    • Local Convergence (see paper)
  • Discussion
analysis of overlay path latency
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)
which is more effective fns or frs
Which is more effective, FNS or FRS?

Plain << FRS << FNS ≈ FNS+FRS

Neighbor Selection is much better than Route Selection

does geometry affect performance of fns or frs
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

summary of results
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
limitations future work
Limitations (future work)
  • Not considered all Geometries
  • Not considered other factors that might matter
    • algorithmic details, symmetry in routing table entries
  • Not considered all performance metrics
conclusions
Conclusions
  • Routing Geometry is a fundamental design choice
    • Geometry determines flexibility
    • Flexibility improves resilience and proximity
  • Ring has the greatest flexibility
    • great routing performance

Why not the Ring?