Ulysses: A Robust, LowDiameter, LowLatency PeertoPeer Network

1
Ulysses A Robust, Low-Diameter, Low-Latency
Peer-to-Peer Network

• Abhishek Kumar
• Shashidhar Merugu
• Jim Xu
• Xingxing Yu
• Georgia Tech.

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Outline

• Review of DHT based search.
• Why worry about Diameter?
• The Butterfly Topology and its p2p version.
• Ulysses - Structure and Operation.
• Simulation Results.

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Distributed Hash table (DHT)
I have foo.doc
HASH(foo.doc)10110
Insert(10110, 67.170.23.25)
67.170.23.25
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Search in a DHT
Foo.doc ?
HASH(foo.doc)10110
Search(10110)
67.170.23.25
67.170.23.25
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Why is diameter so important ?

• One Hop in overlay End to end path
  in underlying network.
• Diameter Worst case latency.
• Avg. hops in overlay avg. latency.
• Littles law
• Avg. hops in overlay avg. stress.
• Reduction in diameter reduces
• Latency
• Node stress
• Edge stress

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Routing table size vs diameter
Routing table size
Maintain full state
n log n ltd
Plaxton et.al, Chord, Pastry, Tapestry
Ulysses, de Bruijn Graph (Koorde etc.)
Viceroy (d7)
Maintain no state
SCAN
0
Worst case distance
O(1) O(log n) O(dn1/d)
O(n)
O(loglognn)
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The Butterfly topology
Source Level
Destination Level
Intermediate Levels
S
Horizontal Links
D
Cross Links
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The p2p Butterfly topology
S
Number of levelsk Out-degree of each
noder Number of nodes in each levelrk Total
nodes in the network, n krk
D

• for n16,000,000 k5 r20 lt log n

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The Butterfly topology
Level 1
Level 0
Level 0
00
00
00
01
01
01
10
10
10
11
11
11
10
The Butterfly topology
Level 1
Level 0
Level 0
00
00
00
01
01
01
10
10
10
11
11
11
Dimension 0
Dimension 1
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The Butterfly topology - with dynamic joins and
departures
Level 0
Level 1
Level 0
00
00
00
01
01
01
100
101
10
10
11
11
11

• Invariant Fanouts are consistent

• Routing still correct and efficient

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Keys in the Ulysses network
1100010100011,2
Level
Row identifier
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Partitioning the keyspace
I want to join
New node
Original node
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Partitioning the keyspace
New node
Take half my Zone
Original node
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Partitioning the keyspace
bit_1 0 1
Original node
New node
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Partitioning the keyspace
bit_1 0 0 1 1
bit_3 0 1 0 1
bit_2 0 0 1 1
bit_4 0 1 0 1
00110101110
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The Ulysses network Links
x
1
x
0
Level 0
Level 0
Level 1
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The Ulysses network Links
x
1
x
0
Level 0
Level 0
Level 1
19
The Ulysses network Links
x
1
x
0
Level 0
Level 0
Level 1
20
The Ulysses network Links
x
1
x
0
Level 0
Level 0
Level 1
21
Routing in the Ulysses network
x
1
x
0
S
D
Level 0
Level 0
Level 1
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Results Reduction in diameter
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Prob. Distribution of no. of hops required to
route a query in a 4 million node network
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Reduction in Stress
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Concluding remarks

• Ulysses achieves the optimum diameter.
• Reduction in diameter reduces
• Latency
• Node stress
• Edge stress
• The complete protocol is also
• Robust can route queries even with node
  failures.
• Self-stabilizing repairs itself on node
  arrivals and departures.