Keeping Wireless Network
Theory Useful
Nancy Lynch, MIT EECS, CSAIL
WRAWN workshop
Montreal, July, 2013
Wireless Network Models
• Purely graph-based models
– Radio Broadcast (protocol) model
– Dual Graph model
𝐺 = (𝑉, 𝐸)
𝐺 = (𝑉, 𝐸, 𝐸)
𝐸  𝐸
Wireless Network Models
• Purely graph-based models
– Radio Broadcast (protocol) model
– Dual Graph model
• Geometry-based models
– Unit Disk Graph (UDG)
– Quasi-Unit-Disk Graph
– Signal-to-Noise Ratio (SiNR)
• Q: Are these models “realistic”?
• In many ways, they are quite strong:
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Graphs derived from geometry in stylized ways.
Mostly reliable.
Mostly static.
Known graphs and geometry (sometimes).
So Are These Models Realistic?
• It depends on the settings and applications
we want to consider.
• Potential wireless network applications:
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Hazardous waste cleanup
Search and rescue
Military operations
Exploring an unknown terrain
Cooperative construction
Flash mob dancing
So Are These Models Realistic?
• It depends on the settings and applications
we want to consider.
• Potential wireless network applications:
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Hazardous waste cleanup
Search and rescue
Military operations
Exploring an unknown terrain
Cooperative construction
Flash mob dancing
• Biological systems:
– Insect colonies
– Cells during
development
– Brains
Algorithm Characteristics
• Algorithms should be efficient (in terms of time, storage,
and communication).
• Algorithms should be flexible:
– They should work in many different settings,.
– Participating nodes should not need to know very much about
the setting.
• Algorithms should be robust to limited amounts of failure
and recovery.
• 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
• Efficient.
• Flexible, Robust, Adaptive
• Q: Why should we focus on these kinds of algorithms?
• A: They correspond to many (most) real wireless settings.
• A: They also correspond to biological systems (insect colonies,
cells during development, brains), which might provide
inspiration for new wireless algorithms.
• We need new theory for these algorithms:
New Theory
• New models that can describe the new platforms
and algorithms.
• New kinds of problem statements.
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New complexity measures that take change into account.
New kinds of algorithms, new analysis methods.
New lower bounds that depend on the additional requirements.
New concurrency theory foundations.
• Problem guarantees will typically be approximate and
probabilistic, not exact and absolute.
• Costs of solving the problems will be inherently higher if we
include requirements of flexibility and robustness.
New Theory
• New models that can describe the new platforms
and algorithms.
• New kinds of problem statements.
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New complexity measures that take change into account.
New kinds of algorithms, new analysis methods.
New lower bounds that depend on the additional requirements.
New concurrency theory foundations.
• Algorithms may be simpler, more “self-organizing” than usual.
• 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
• Dual Graph model [Kuhn, Lynch, Newport
DISC 09]
– Collisions result in message loss.
– Unreliable and reliable edges.
– Dynamic: Message reach varies over time.
• 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
• Algorithms are more costly than for the
radio broadcast model.
• Adaptive to dynamic uncertainty of
message reach.
• Partially flexible: Nodes use partial
knowledge of the networks.
• Not robust.
• 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
• Some work on higher-level algorithms in wireless networks assumes
completely reliable local broadcast (RLB) communication.
• Examples:
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Global broadcast in static graph networks
Building network structures
Computing in dynamic graph networks
Robot coordination
• Abstract MAC layers [Kuhn, Lynch, Newport 09], mask low-level
wireless communication, yield RLB guarantees.
• But low-level wireless protocols do not guarantee completely reliable
local broadcast.
– They involve probabilistic transmission, random backoff, random coding,…
– Yield high-probability guarantees only.
• So we defined a probabilistic abstract MAC layer [Khabbazian,
Kowalski, Kuhn, Lynch DIALM-POMC 10].
– Fast delivery of each message to all neighbors whp.
– Each receiver receives some message quickly whp.
High-Level Wireless Communication
and Computation
• Questions:
– Design 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?
• Problems to consider:
– Communication, building network structures.
– Robot problems: task allocation, forming geometric patterns,
exploration/routing/navigating.
• Also consider other kinds of failures, mobility.
• Combine these considerations with Dual Graph issues.
3. Social Insect Colonies
• Social insects (ants and bees) live in colonies, cooperate to solve
complex problems, including:
– Division of labor (foraging for food, feeding larvae, cleanup,
defense,…)
– Searching/routing/navigating.
– Agreeing on the site of a new nest.
– Constructing nests.
• They use distributed algorithms, based on direct chemical or
physical communication, or on leaving chemical signals in the
environment (stigmergy).
• Algorithms are highly flexible, robust, and
adaptive.
• Efficient: Colonies perform their work
quickly, with low energy usage.
Social Insect Colonies
• 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.
• Robust:
– Death of some insects doesn’t affect the colony much.
– Destroying the nest leads the insects to find/build another nest.
– Homeostasis?
• Adaptive to changes to the colony, to the
environment.
Proposed Research Project
• Dornhaus (insect colony bio), Lynch (dist. algs.), Nagpal (robotics)
• Distributed Problem Solving in Dynamic Collectives: Theory, Insects,
and Robots
• Identify/analyze distributed algorithms that may be used by insect
colonies.
• Define platform models, problems, algorithms.
• Examples: Division of labor, foraging, nest construction.
• Contributions to insect colony research:
– Discover what algorithms insects actually use, and why.
– Analyze the algorithms based on performance plus adaptivity.
• Contributions to (wireless) distributed algorithms:
– New adaptive algorithms, inspired by insect colony behavior.
– New measures and analysis methods, for adaptive algorithms.
– New concurrency theory.
• Contributions to robotics:
– Adapt insect algorithms for robot swarms.
4. Developing organisms
• Cells in a developing embryo cooperate to solve problems
of patterning.
• Sometimes involves scaling.
• They use distributed algorithms, based on:
– Local chemical signaling between cells.
• Like “beep” communication, as studied in our community.
– Global morphogen gradients [Turing].
• Simple local rules.
• Flexible: Not dependent on exact
number of cells, size of organism.
• Robust: Death of some cells doesn’t
matter much; homeostasis.
Developing organisms
• Questions: Identify/analyze distributed algorithms that
may be used by cells in developing organisms.
• Define platform models, problems, algorithms.
• Contributions to developmental biology:
– Discover what algorithms developing organisms actually use, and why.
– Analyze algorithms based on performance, robustness to failures
• Contributions to (wireless) distributed algorithms:
– New algorithms, inspired by developmental behavior.
– New measures and analysis methods
– New concurrency theory.
• In general, understanding biological
algorithms could help us understand how
to build simple, efficient, flexible, robust,
adaptive wireless network algorithms.
Summary: Needed Work
• Research on algorithms for wireless networks
that are flexible, robust, and adaptive to
changes.
• New kinds of models, cost metrics
• New kinds of algorithms
• New kinds of analysis
Concurrency theory foundations
• General models based on interacting automata.
• Must include time, discrete + continuous behavior,
motion, probability.
• Composition, abstraction.
• Tailor for wireless systems.
Thank you!