slides - Workshop on Realistic Models for Algorithms in Wireless ...

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Nov 24, 2013 (3 years and 4 months ago)

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Keeping Wireless Network
Theory Useful

Nancy Lynch, MIT EECS, CSAIL

WRAWN workshop

Montreal, July, 2013

Wireless Network Models

β€’
Purely graph
-
based models

–
Radio Broadcast (protocol) model

–
Dual Graph model


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Wireless Network Models

β€’
Purely graph
-
based models

–
Radio Broadcast (protocol) model

–
Dual Graph model

β€’
Geometry
-
based models

–
Unit Disk Graph (UDG)

–
Quasi
-
Unit
-
Disk Graph

–
Signal
-
to
-
Noise Ratio (
SiNR
)

β€’
Q:
Are these models β€œrealistic”?

β€’
In many ways, they are quite strong:

–
Graphs derived from geometry in stylized ways.

–
M
ostly reliable.

–
Mostly static.

–
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:

–
Hazardous waste cleanup

–
Search and rescue

–
Military operations

–
Exploring an unknown terrain

–
Cooperative construction

–
Flash mob dancing

β€’
It depends on the settings and applications
we want to consider.

β€’
P
otential wireless network applications:

–
Hazardous waste cleanup

–
Search and rescue

–
Military operations

–
Exploring an unknown terrain

–
Cooperative construction

–
Flash mob dancing

β€’
Biological systems:

–
Insect colonies

–
Cells during
development

–
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
:

–
T
hey should
work in
many different settings,.

–
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.:

–
The set of participating nodes may change (join, leave, fail,
recover) during execution.

–
Communication is subject to uncertainty, success may vary during
execution.

–
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 β€œself
-
organizing” 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]

–
Collisions result in message loss.

–
Unreliable and reliable edges.

–
Dynamic: Message reach varies over time.

β€’
Example algorithms
using Dual Graphs:

–
Building Dominating
Sets,
MISs
[
K,L,N
,
Oshman
,
Richa

PODC 10]

–
Local and global
broadcast
[
Ghaffari
,
Haeupler
,
L,N
DISC 12
]

–
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:

–
Consider more dynamic behavior:
Failures
. Mobility.

–
Can we get good bounds for
local/global broadcast
in such highly
dynamic
settings?

–
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:

–
Global broadcast in static graph networks

–
Building network structures

–
Computing in dynamic graph networks

–
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.

–
They involve probabilistic transmission, random
backoff
, random coding,…

–
Y
ield high
-
probability guarantees only.

β€’
So we defined a
probabilistic abstract MAC layer
[
Khabbazian
,
Kowalski, Kuhn, Lynch DIALM
-
POMC 10].

–
F
ast delivery of each message to all neighbors
whp
.

–
E
ach receiver receives some message quickly
whp
.

High
-
Level Wireless Communication
and Computation

β€’
Questions:

–
D
esign algorithms above
a

local
bcast

layer that tolerate occasional
exceptions (lost messages).

–
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?

–
What are inherent limitations?

–
How do we model/verify compositions of high
-
level probabilistic
algorithms and probabilistic implementations of local broadcast?

β€’
Problems to consider:

–
Communication, building network structures.

–
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:

–
D
ivision of labor (foraging for food, feeding larvae, cleanup,
defense,…)

–
Searching/routing/navigating.

–
Agreeing on the site of a new nest.

–
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:

–
Insects don’t know the exact size of the colony, though they may
have a rough idea.

–
Insects don’t know all the details of their physical environment.

–
But colonies may have evolved to do better in certain kinds of
settings than others.

β€’
Robust:

–
Death of some insects doesn’t affect the colony much.

–
Destroying the nest leads the insects to find/build another nest.

–
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:

–
Discover what algorithms insects actually use, and why.

–
Analyze the algorithms based on performance plus
adaptivity
.

β€’
Contributions to (wireless) distributed algorithms:

–
New adaptive algorithms, inspired by insect colony behavior.

–
New measures and analysis methods, for adaptive algorithms.

–
New concurrency theory.

β€’
Contributions to robotics:

–
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:

–
Local chemical signaling between cells.

β€’
Like β€œbeep” communication, as studied in our community.

–
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 doesn’t
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:

–
Discover what algorithms
developing organisms actually
use, and why.

–
Analyze algorithms
based on
performance, robustness
to
failures

β€’
Contributions to (wireless) distributed algorithms:

–
New
algorithms
, inspired by
developmental behavior
.

–
New measures and analysis
methods

–
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!