Keeping Wireless Network Theory Useful

1. Keeping Wireless Network Theory Useful Nancy Lynch, MIT EECS, CSAIL WRAWN workshop Montreal, July, 2013

2. Wireless Network Models • Purely graph-based models • Radio Broadcast (protocol) model • Dual Graph model 

3. 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).

4. 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

5. 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 • Biological systems: • Insect colonies • Cells during development • Brains

6. 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.

7. 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:

8. 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.

9. 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.

10. Examples

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

12. 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]

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?

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.

20. 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, adaptivewireless network algorithms.

21. 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

22. Concurrency theory foundations • General models based on interacting automata. • Must include time, discrete + continuous behavior, motion, probability. • Composition, abstraction. • Tailor for wireless systems.

23. Thank you!