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Keeping Wireless Network Theory Useful

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Keeping Wireless Network Theory Useful

Nancy Lynch, MIT EECS, CSAIL

WRAWN workshop

Montreal, July, 2013

- Purely graph-based models
- Radio Broadcast (protocol) model
- Dual Graph model

- 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).

- 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

- 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.

- 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 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 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.

- Low-level wireless communication
- High-level wireless communication and computation.
- Social insect colonies
- Developing organisms

- 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]

- 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?

- 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.

- 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.

- 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.

- 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.

- 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.

- 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].

- Local chemical signaling between cells.

- Simple local rules.
- Flexible: Not dependent on exact number of cells, size of organism.
- Robust: Death of some cells doesn’t matter much; homeostasis.

- 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, adaptivewireless network algorithms.

- 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

- General models based on interacting automata.
- Must include time, discrete + continuous behavior, motion, probability.
- Composition, abstraction.
- Tailor for wireless systems.