Algorithmic Models of
Wireless Communication
Magnús M. Halldórsson
Reykjavik University, Iceland
EWSCS, 7 March,2013
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It’s Wireless World
GSM
3G
WiFi
P2P
WiMax
Ad-hoc
Mobility
Sensor
networks
Ambient
Ubiquitous
Pervasive
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Algorithmic Agenda
• How to model wireless communication
– Particularly, interference
– Capture realism
– Analytically feasible
• How to solve fundamental problems
– Algorithmic strategies
– Structural properties
• Modus operandi:
– Ignore constant factors
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MODELS OF INTERFERENCE
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Tradeoffs in Models
Realism
Generality
Models
Usability
for
algorithms
Usability
for
analysis
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Models for Interference
•
Two standard models in wireless networking
Protocol Model
(graph-based, simpler)
Physical Model
(SINR-based, more realistic)
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CS Models: e.g. Disk Model (Protocol Model)
Reception
Range
Interference
Range
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Inductive independence
• There is a disc that intersects at most 3 mutually non-overlapping
discs
• Efficient 3-approximate algorithms for:
– Independent set (maximize throughput)
– Coloring
(minimize latency)
– Weighted independent set (maximize sustained throughput)
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EE Models: e.g. SINR Model (Physical Model)
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Hard instances for traditional graph-based models
• One link per slot, in graph-based models
• Single slot, in physical model (with appropriate power control)
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Signal transmission
• Radio signal diminishes as it travels

• In the ideal case, the path loss is proportional to
where
d : distance
 : path loss constant (usually, 2 <  < 6), depends on medium
d
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=2
Uniform power
Affectance
u
2
3.5
u
0.16
5
5
w
1 / 3.5
au ( w) 
 2.04

1/ 5
2.04
w
1 / 5
aw (u ) 
 0.16

1/ 2
H, Wattenhofer ‘09
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=2
Power control
Affectance
u
2
Pu = 1
3.5
u
0.48
5
5
Pw = 3
w
1 / 3.5
au ( w) 
 0.68

3/ 5
0.68
w
3 / 5
aw (u ) 
 0.48

1/ 2
H, Wattenhofer ‘09
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=2
Affectance
v
u
3
3
u
0.56
4
4
0.56
3
w
w
1 / 42
au ( w) 
 0.56
2
1/ 3
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Core problems of wireless scheduling
• Given: A set of communication links
Capacity problem:
Find the maximum size feasible subset of links
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Core problems of wireless scheduling
• Given: A set of communication links
Capacity problem:
Find the maximum size feasible subset of links
Scheduling problem:
Partition the links into fewest possible slots
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The job of the MAC layer
• MAC : Media Access Control
• The nodes in a wireless
network communicate over a
shared resource: the spectrum
• The task of the MAC layer is to
coordinate access to the
spectrum:
– Who gets to talk when
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Results on Capacity and Scheduling
Capacity has constant-factor approximations for:
• Uniform power in R2, with >2.
[Goussevskaia,H,Wattenhofer,Welzl‘09]
• Any (reasonable) fixed power in general metrics [H, Mitra, SODA‘11]
• Arbitrary power control [Kesselheim, SODA‘11]
– Also, more recently, with power limitations [Wan‘12, Kesselheim‘12]
• Uniform power with spectrum sharing (cognitive radio) [H,Mitra‘12]
• Fixed power with variable data rates [Kesselheim‘12]
• Uniform power with a distributed learning algorithm [Asgeirsson,
Mitra ‚‘11]
Scheduling has constant-factor approximation for:
• Linear power [Fanghanel,Kesselheim,Vöcking’09; Tonoyan‘11]
• Equal-length links [Goussevskaia,Oswald,Wattenhofer, ’07; H ‘09]
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Weighted degree
of v
Weighted inductiveness
• A link lv in a set S is t-good if av(S)+aS(v) ≤ t.
• A set of links is is t-inductive independent
if any subset contains a t-good link
• [H, Holzer, Mitra, Wattenhofer, SODA’13]
Any set of links in any metric is O(1)-inductive independent,
except possibly when using uniform power.
• Applications:
–
–
–
–
–
Capacity algorithms
(Multi-hop) distributed scheduling
Connectivity
Spectrum sharing auctions [Hoefer, Kesselheim, Vöcking ‘11,‘12]
Dynamic packet scheduling
Kesselheim, Vöcking, DISC‘10
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EXPERIMENTAL WORK
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Experimental Work
„Putting theory to the test“
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Testbed experimentation
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Experimental Group
Ýmir Vigfússon
Students
Helga Guðmundsóttir
Henning Úlfarsson
Eyjólfur Ingi
Ásgeirsson
Joe Foley
Sveinn Fannar
Kristjánsson
Axel Guðmundsson
Sindri Magnússon
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Theory Group
• Pradipta Mitra, post-doc
• Marijke Bodlaender, Ph.D. student
• Hörður Ingi Björnsson, M.S. student
• Eyjólfur
Henning
• Magnús
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Other Collaborators
• Sverrir Ólafsson, prófessor, Reykjavik University
– Previously at British Telecom
• Roger Wattenhofer, prófessor, ETH Zurich
• Berthold Vöcking, prófessor, TU Aachen
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Questions?
Slides: Thanks to Wattenhofer Lab, ETH
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