where theory meets practice · ec sensys osdi mobicom multimedia ubicomp sigcomm hotnets wireless...
TRANSCRIPT
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ETH Zurich – Distributed Computing – www.disco.ethz.ch
Roger Wattenhofer
Sensor Networks Where Theory Meets Practice
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Theory Meets Practice
PODC
SODA
STOCFOCS
ICALPSPAA
EC
SenSysOSDI
Mobicom
Multimedia
Ubicomp
SIGCOMM
HotNets
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Wireless Communication?
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Capacity!
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InterferenceRange
Protocol Model
ReceptionRange
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6
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Physical (SINR) Model
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Signal-To-Interference-Plus-Noise Ratio (SINR) Formula
Minimum signal-to-interference
ratio
Power level of sender u
Path-loss exponent
Noise
Distance betweentwo nodes
Received signal power from sender
Received signal power from all other nodes (=interference)
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Example: Protocol vs. Physical Model
1m
Assume a single frequency (and no fancy decoding techniques!)
Let =3, =3, and N=10nW
Transmission powers: PB= -15 dBm and PA= 1 dBm
SINR of A at D:
SINR of B at C:
4m 2m
A B C D
Is spatial reuse possible?
NO Protocol Model
YES With power control
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This works in practice
… even with very simple hardware
Time for transmitting 20‘000 packets:
Speed-up is almost a factor 3
u1 u2 u3 u4 u5 u6
[Moscibroda, W, Weber, Hotnets 2006]
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Possible Application – Hotspots in WLAN
X
Y
Z
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Possible Application – Hotspots in WLAN
X
Y
Z
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The Capacity of a Network(How many concurrent wireless transmissions can you have)
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Convergecast Capacity in Wireless Sensor Networks
15
Protocol Model
Physical Model (power control)
Max. rate in arbitrary, worst-case deployment
(1/𝑛)
(1/log3 𝑛)
Max. rate in random, uniform deployment
(1/log 𝑛)
(1/log 𝑛)
Worst-Case Capacity
Topology
Model/Power
Classic Capacity
[Giridhar, Kumar, 2005][Moscibroda, W, 2006]
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Capacity of a Network
Classic Capacity Worst-Case Capacity
How much information can betransmitted in nice networks?
How much information can betransmitted in nasty networks?
How much information can betransmitted in any network?
Real Capacity
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Core Capacity Problems
Given a set of arbitrary communication links
One-Shot ProblemFind the maximum size feasible subset of links
O(1) approximations for uniform power [Goussevskaia, Halldorsson, W, 2009 & 2014] as well as arbitrary power [Kesselheim, 2011]
Scheduling ProblemPartition the links into fewest possible slots, to minimize time
Open problem: Only 𝑂(log𝑛) approximation using the one-shot subroutine
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The Capture Effect
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Receiving Different Senders
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Layer 4
Layer 3
Layer 2
Layer 1
-64 dBm
-70 dBm
-75 dBm
-81 dBm
“Layer” Abstraction
[König, W, 2016]
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Constructive Interference
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Energy Efficiency?
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Clock Synchronization!
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Clock Synchronization Example: Dozer
• Multi-hop sensor network with duty cycling• 10 years of network life-time, mean energy consumption: 0.066mW• High availability, reliability (99.999%)• Many different applications use Dozer: TinyNode, PermaSense, etc.
[Burri, von Rickenbach, W, 2007]
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Problem: Physical Reality
t
clock rate
11 + 𝜀
message delay
1 − 𝜀
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Given a communication network
1. Each node equipped with hardware clock with drift
2. Message delays with jitter
Goal: Synchronize Clocks (“Logical Clocks”)
• Both global and local synchronization!
Clock Synchronization in Theory?
worst-case (but constant)
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• Time (logical clocks) should not be allowed to stand still or jump
Time Must Behave!
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Local Skew
Tree-based Algorithms Neighborhood Algorithms
e.g. FTSP e.g. GTSP
Bad local skew
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Synchronization Algorithms: An Example (“Amax”)
• Question: How to update the logical clock based on the messages from the neighbors?
• Idea: Minimizing the skew to the fastest neighbor
– Set clock to maximum clock value you know, forward new values immediately
• First all messages are slow (1), then suddenly all messages are fast (0)!
Time is T Time is T
…
Clock value:
T
Clock value:
T-1
Clock value:
T-D+1
Clock value:
T-D
Time is T
skew D
Fastest
Hardware
Clock
T T
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Dynamic Networks![Kuhn et al., PODC 2010]
Local Skew: Overview of Results
1 logD √D D …
Everybody‘s expectation, 10 years ago („solved“)
Lower bound of logD / loglogD[Fan & Lynch, PODC 2004]
All natural algorithms [Locher et al., DISC 2006]
Blocking algorithm
Kappa algorithm[Lenzen et al., FOCS 2008]
Tight lower bound[Lenzen et al., PODC 2009]
Dynamic Networks![Kuhn et al., SPAA 2009]
together[JACM 2010]
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Experimental Results for Global Skew
FTSP PulseSync
[Lenzen, Sommer, W, 2014]
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Experimental Results for Global Skew
FTSP PulseSync
[Lenzen, Sommer, W, 2014]
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Network Dynamics?
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Distributed Control!
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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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(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, 2016]
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SublinearAlgorithms
Self-Stabilization
Self-Assembly
Applicationse.g. Multi-Core
Dynamic (e.g. Ad Hoc)Networks
DistributedComplexity
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SublinearAlgorithms
Self-Stabilization
Self-Assembly
Applicationse.g. Multi-Core
Dynamic(e.g. Ad Hoc)Networks
DistributedComplexity
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Summary
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The Capture Effect
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How many lines of pseudo code Can you implement on a sensor node?
The best algorithm is often complexAnd will not do what one expects.
Theory models made lots of progressReality, however, they still don’t address.
My advice: invest your research £££sin ... impossibility results and lower bounds!
Theory for sensor networks, what is it good for?!
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Thank You!Questions & Comments?
Thanks to my co-authors, mostlySilvio FrischknechtMagnus HalldorssonStephan HolzerMichael KönigChristoph LenzenThomas MoscibrodaPhilipp Sommer www.disco.ethz.ch