Algorithmic Models of Wireless Communication

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Algorithmic Models of Wireless Communication

• Magnús M. Halldórsson
• Reykjavik University, Iceland

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Its Wireless World
GSM
3G
P2P
WiMax
WiFi
? Wireless communication
Ad-hoc
Sensor networks
Mobility
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
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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)
ReceptionRange
InterferenceRange
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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
  towhere d distance ? path loss
  constant (usually, 2 lt ? lt 6), depends on medium

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Affectance
Uniform power
?2
u
2
3.5
5
5
w
 
H, Wattenhofer 09
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Affectance
Power control
?2
u
2
Pu 1
3.5
5
5
w
Pw 3
H, Wattenhofer 09
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Affectance
?2
v
u
3
3
4
4
3
w
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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 ?gt2.
  Goussevskaia,H,Wattenhofer,Welzl09
• Any (reasonable) fixed power in general metrics
  H, Mitra, SODA11
• Arbitrary power control Kesselheim, SODA11
• Also, more recently, with power limitations
  Wan12, Kesselheim12
• Uniform power with spectrum sharing (cognitive
  radio) H,Mitra12
• Fixed power with variable data rates
  Kesselheim12
• Uniform power with a distributed learning
  algorithm Asgeirsson, Mitra 11
• Scheduling has constant-factor approximation for
• Linear power Fanghanel,Kesselheim,Vöcking09
  Tonoyan11
• Equal-length links Goussevskaia,Oswald,Wattenhofe
  r, 07 H 09

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Weighted inductiveness
Weighted degree of v

• 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, SODA13 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, DISC10
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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

• Students

Ýmir Vigfússon
Helga Guðmundsóttir
Henning Úlfarsson
Sveinn Fannar Kristjánsson
Eyjólfur Ingi Ásgeirsson
Axel Guðmundsson
Sindri Magnússon
Joe Foley
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Theory Group

• Pradipta Mitra, post-doc
• Marijke Bodlaender, Ph.D. student
• Hörður Ingi Björnsson, M.S. student
• Eyjólfur
• Magnús

Henning
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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?
Thank you
Post-doc Ph.D. positions available
Slides Thanks to Wattenhofer Lab, ETH