Keeping Wireless Network
Theory Useful
Nancy Lynch, MIT EECS, CSAIL
WRAWN workshop
Montreal, July, 2013
Wireless Network Models
β’
Purely graph

based models
β
Radio Broadcast (protocol) model
β
Dual Graph model
πΊ
=
(
π
,
πΈ
)
πΊ
=
(
π
,
πΈ
,
πΈ
ο’
)
πΈ
ο
πΈ
ο’
Wireless Network Models
β’
Purely graph

based models
β
Radio Broadcast (protocol) model
β
Dual Graph model
β’
Geometry

based models
β
Unit Disk Graph (UDG)
β
Quasi

Unit

Disk Graph
β
Signal

to

Noise Ratio (
SiNR
)
β’
Q:
Are these models βrealisticβ?
β’
In many ways, they are quite strong:
β
Graphs derived from geometry in stylized ways.
β
M
ostly reliable.
β
Mostly static.
β
Known graphs and geometry (sometimes).
So Are These Models Realistic?
β’
It depends on the settings and applications
we want to consider.
β’
P
otential wireless network applications:
β
Hazardous waste cleanup
β
Search and rescue
β
Military operations
β
Exploring an unknown terrain
β
Cooperative construction
β
Flash mob dancing
β’
It depends on the settings and applications
we want to consider.
β’
P
otential wireless network applications:
β
Hazardous waste cleanup
β
Search and rescue
β
Military operations
β
Exploring an unknown terrain
β
Cooperative construction
β
Flash mob dancing
β’
Biological systems:
β
Insect colonies
β
Cells during
development
β
Brains
So Are These Models Realistic?
Algorithm Characteristics
β’
Algorithms should be
efficient
(in terms of time, storage,
and communication).
β’
Algorithms
should be
flexible
:
β
T
hey should
work in
many different settings,.
β
P
articipating nodes should not need to
know
very
much about
the
setting.
β’
Algorithms should
be
robust
to
limited amounts of failure
and
recovery.
β’
More generally, algorithms should be
adaptive to changes
during execution
, e.g.:
β
The set of participating nodes may change (join, leave, fail,
recover) during execution.
β
Communication is subject to uncertainty, success may vary during
execution.
β
Nodes may move, connectivity may change.
Algorithm Characteristics
β’
Efficient.
β’
Flexible
, Robust,
Adaptive
β’
Q:
Why should we focus on these kinds of algorithms?
β’
A:
They
correspond to
many (most
)
real wireless
settings.
β’
A:
They
also correspond to
biological systems (insect colonies,
cells during development, brains), which might provide
inspiration for new wireless algorithms.
β’
We need new theory for these algorithms:
New Theory
β’
New models
that can describe
the new platforms
and algorithms.
β’
New kinds of problem statements.
β’
New complexity measures that take change into account.
β’
New
kinds of algorithms,
new analysis methods.
β’
New lower bounds that depend on the additional requirements.
β’
New concurrency theory foundations
.
β’
Problem guarantees will typically be approximate and
probabilistic, not exact and absolute.
β’
Costs of solving the problems will be inherently higher if we
include requirements of flexibility and robustness.
New Theory
β’
New models
that can describe
the new platforms
and algorithms.
β’
New kinds of problem statements.
β’
New complexity measures that take change into account.
β’
New
kinds of algorithms,
new analysis methods.
β’
New lower bounds that depend on the additional requirements.
β’
New concurrency theory foundations
.
β’
Algorithms may be simpler, more βself

organizingβ than usual.
β’
Foundations based on Probabilistic Timed I/O Automata
.
Examples
Examples
1.
Low

level wireless communication
2.
High

level wireless communication and
computation.
3.
Social insect colonies
4.
Developing organisms
1. Low

Level Wireless Communication
β’
Dual Graph model
[Kuhn, Lynch, Newport
DISC 09]
β
Collisions result in message loss.
β
Unreliable and reliable edges.
β
Dynamic: Message reach varies over time.
β’
Example algorithms
using Dual Graphs:
β
Building Dominating
Sets,
MISs
[
K,L,N
,
Oshman
,
Richa
PODC 10]
β
Local and global
broadcast
[
Ghaffari
,
Haeupler
,
L,N
DISC 12
]
β
Reasonably efficient algorithms for local and global broadcast,
provided message
reach is determined by an oblivious adversary,
and some geographical constraints are satisfied
[
Ghaffari
, Lynch,
Newport PODC 13]
Low

Level Wireless Communication
β’
Algorithms are more costly than for the
radio broadcast model.
β’
Adaptive
to dynamic uncertainty of
message reach.
β’
Partially flexible
: Nodes use partial
knowledge of the
networks.
β’
Not robust
.
β’
Questions:
β
Consider more dynamic behavior:
Failures
. Mobility.
β
Can we get good bounds for
local/global broadcast
in such highly
dynamic
settings?
β
What are the limits of flexibility? That is, what knowledge of the
networks is actually required to solve problems using this model?
2. High

Level Wireless Communication
and Computation
β’
Some work on higher

level algorithms in wireless networks assumes
completely reliable local broadcast (RLB) communication.
β’
Examples:
β
Global broadcast in static graph networks
β
Building network structures
β
Computing in dynamic graph networks
β
Robot coordination
β’
Abstract MAC layers
[Kuhn, Lynch, Newport 09],
mask low

level
wireless communication, yield RLB guarantees.
β’
But low

level wireless protocols do not guarantee completely reliable
local broadcast.
β
They involve probabilistic transmission, random
backoff
, random coding,β¦
β
Y
ield high

probability guarantees only.
β’
So we defined a
probabilistic abstract MAC layer
[
Khabbazian
,
Kowalski, Kuhn, Lynch DIALM

POMC 10].
β
F
ast delivery of each message to all neighbors
whp
.
β
E
ach receiver receives some message quickly
whp
.
High

Level Wireless Communication
and Computation
β’
Questions:
β
D
esign algorithms above
a
local
bcast
layer that tolerate occasional
exceptions (lost messages).
β
Which currently

existing high

level algorithms, written over a RLB
layer, already tolerate such exceptions, or can
easily be
modified
to
do
so? Which do not?
β
What are inherent limitations?
β
How do we model/verify compositions of high

level probabilistic
algorithms and probabilistic implementations of local broadcast?
β’
Problems to consider:
β
Communication, building network structures.
β
R
obot
problems: task allocation, forming geometric patterns,
exploration/routing/navigating
.
β’
Also consider other kinds of failures, mobility.
β’
C
ombine these considerations with Dual Graph issues.
3. Social Insect Colonies
β’
Social insects (ants and bees) live in colonies, cooperate to solve
complex problems, including:
β
D
ivision of labor (foraging for food, feeding larvae, cleanup,
defense,β¦)
β
Searching/routing/navigating.
β
Agreeing on the site of a new nest.
β
Constructing nests.
β’
They use distributed algorithms, based on direct chemical or
physical communication, or on leaving
chemical
signals in the
environment (
stigmergy
).
β’
Algorithms are
highly flexible, robust, and
adaptive.
β’
Efficient: Colonies perform their work
quickly, with low energy usage.
Social Insect Colonies
β’
Flexible:
β
Insects donβt know the exact size of the colony, though they may
have a rough idea.
β
Insects donβt know all the details of their physical environment.
β
But colonies may have evolved to do better in certain kinds of
settings than others.
β’
Robust:
β
Death of some insects doesnβt affect the colony much.
β
Destroying the nest leads the insects to find/build another nest.
β
Homeostasis?
β’
Adaptive to changes to the colony, to the
environment.
Proposed Research Project
β’
Dornhaus
(insect colony
bio),
Lynch
(dist.
a
lgs
.),
Nagpal
(robotics)
β’
Distributed Problem Solving in Dynamic Collectives: Theory, Insects,
and Robots
β’
Identify/analyze
distributed algorithms
that may be used
by insect
colonies
.
β’
D
efine platform models, problems, algorithms.
β’
Examples:
D
ivision of labor, foraging, nest construction.
β’
Contributions to insect colony research:
β
Discover what algorithms insects actually use, and why.
β
Analyze the algorithms based on performance plus
adaptivity
.
β’
Contributions to (wireless) distributed algorithms:
β
New adaptive algorithms, inspired by insect colony behavior.
β
New measures and analysis methods, for adaptive algorithms.
β
New concurrency theory.
β’
Contributions to robotics:
β
Adapt insect algorithms for robot swarms.
4. Developing organisms
β’
Cells in a developing embryo cooperate to solve problems
of patterning.
β’
Sometimes involves scaling.
β’
They use distributed algorithms, based
on:
β
Local chemical signaling between cells.
β’
Like βbeepβ communication, as studied in our community.
β
G
lobal
morphogen
gradients
[Turing].
β’
Simple local rules.
β’
Flexible:
Not dependent on exact
number of cells, size of organism.
β’
Robust:
Death of some cells doesnβt
matter much; homeostasis.
Developing organisms
β’
Questions: Identify/analyze
distributed algorithms that
may be used by
cells in developing organisms.
β’
Define platform models, problems, algorithms.
β’
Contributions to developmental biology:
β
Discover what algorithms
developing organisms actually
use, and why.
β
Analyze algorithms
based on
performance, robustness
to
failures
β’
Contributions to (wireless) distributed algorithms:
β
New
algorithms
, inspired by
developmental behavior
.
β
New measures and analysis
methods
β
New concurrency theory
.
β’
In general, understanding biological
algorithms could help us understand how
to build
simple, efficient, flexible, robust,
adaptive
wireless network algorithms.
Summary: Needed Work
β’
R
esearch on algorithms for wireless networks
that are flexible, robust, and adaptive to
changes.
β’
New kinds of models, cost metrics
β’
New kinds of algorithms
β’
New kinds of analysis
Concurrency theory
f
oundations
β’
General models based on
interacting automata.
β’
M
ust include time
, discrete + continuous behavior
,
motion, probability
.
β’
Composition
, abstraction
.
β’
Tailor for wireless systems.
Thank you!
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