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)

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:

– 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:– Hazardous waste cleanup– Search and rescue– Military operations– Exploring an unknown terrain– Cooperative construction– Flash mob dancing

• It depends on the settings and applications we want to consider.

• Potential wireless network applications:– 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

So Are These Models Realistic?

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.

• 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.

• 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 communication2. High-level wireless communication and

computation.3. Social insect colonies4. 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:– 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!