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ETH Zurich – Distributed Computing – www.disco.ethz.ch
Roger Wattenhofer
Is Network Science a Science?
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Confession
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I don’t have a
account.
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… but I always loved networks*
*Computer NetworksWireless Networks
Social NetworksMobile Networks
Biological NetworksEconomic Networks
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Past SuccessesSome Success Stories of
Network Science
Milgram, Watts-Strogatz,
& Kleinberg
Markov Chains, Stationary Distribution,
& PageRank
Spectral Graph Theory
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But…
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Real Science has (Open) Problems
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Science: Still Interesting in 100 Years
Engineering: Interesting Right Now!
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Complexity Theory
Can a Computer Solve Problem P in Time t?
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Complexity Theory
Can a Computer Solve Problem P in Time t?
Network
Distributed
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Complexity Theory
Can a Computer Solve Problem P in Time t?
Network
NetworkDistributed
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Distributed (Message-Passing) Algorithms
• Nodes are agents with unique ID’s that can communicate with neighbors by sending messages. In each synchronous round, every node can send a (different) message to each neighbor.
69
17
11
10 7
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Distributed (Message-Passing) Algorithms
• Nodes are agents with unique ID’s that can communicate with neighbors by sending messages. In each synchronous round, every node can send a (different) message to each neighbor.
• Distributed (Time) Complexity: How many rounds does problem take?
69
17
11
10 7
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An Example
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How Many Nodes in Network?
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How Many Nodes in Network?
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How Many Nodes in Network?
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How Many Nodes in Network?
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How Many Nodes in Network?
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How Many Nodes in Network?
1
1
1
1
1
1
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How Many Nodes in Network?
2
1
1
2
1
4
1
1
1
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How Many Nodes in Network?
With a simple flooding/echo process, a network can find the numberof nodes in time 𝑂(𝐷), where 𝐷 is the diameter (size) of the network.
2
1
1
2
1
4
1
1
1
10
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Diameter of Network?
• Distance between two nodes = Number of hops of shortest path
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Diameter of Network?
• Distance between two nodes = Number of hops of shortest path
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Diameter of Network?
• Distance between two nodes = Number of hops of shortest path
• Diameter of network = Maximum distance, between any two nodes
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Diameter of Network?
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Diameter of Network?
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Diameter of Network?
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Diameter of Network?
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Diameter of Network?
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Diameter of Network?
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Diameter of Network?
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(even if diameter is just a small constant)
Pair of rows connected neither left nor right? Communication complexity: Transmit Θ(𝑛2) information over O(𝑛) edges Ω(𝑛) time!
[Frischknecht, Holzer, W, 2012]
Networks Cannot Compute Their Diameter in Sublinear Time!
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e.g., dominating set approximation in planar graphs
Distributed Complexity Classification
1 log∗ 𝑛 polylog 𝑛 𝐷 poly 𝑛
various problems in growth-bounded graphs
MIS, approx. of dominating set, vertex cover, ...
count, sum, spanning tree, ...
diameter, MST, verification of e.g. spanning tree, …
e.g., [Kuhn, Moscibroda, W, 2014]
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SublinearAlgorithms
Self-Stabilization
Self-Assembly
Applicationse.g. Multi-Core
DynamicNetworks
DistributedComplexity
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SublinearAlgorithms
Self-Stabilization
Self-Assembly
Applicationse.g. Multi-Core
DynamicNetworks
DistributedComplexity
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Science: Still Interesting in 100 Years
Engineering: Interesting Right Now!
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Bitcoin
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Bank of Bitcoin
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Spending Money
AmountDestination
Signature
Source
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Moving Money
Source Destination Amount
Source Destination Amount
Source Destination Amount
Transaction
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Distributing the Bank
TX
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Propagation Time
[Decker, W, 2013]
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Double-spending
TX
Source Destination Amount
TX’
Source Destination Amount
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Double-spending in the Network
TX TX’
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Distributing the Bank
I am the leader
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Double-spending in the Real World[Bamert, Decker, Elsen, W, Welten, 2013]
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Where would you inject your transaction?
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Double-spending, the Theory
Player 1: Where to inject original transaction?Player 2: Where to inject copy?
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Really?
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Sometimes, being second is better!
[Meier, Pignolet, Schmid, W, 2014]
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Another Example: Nontransitive Dice
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Transaction Malleability
February 10, 2014: “Addressing Transaction Malleability: MtGox has detected unusual activity on its Bitcoin wallets and performed investigations during the past weeks.”
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Transaction Malleability
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Transaction Malleability in Real Life
386 Bitcoins
[Decker, W, Arxiv, in submission ]
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Summary
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Thank You!Questions & Comments?
Thanks to my co-authors, mostlyChristian DeckerSilvio FrischknechtStephan Holzer www.disco.ethz.ch