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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. . Wireless Network Models. Purely graph-based models

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keeping wireless network theory useful

Keeping Wireless Network Theory Useful

Nancy Lynch, MIT EECS, CSAIL

WRAWN workshop

Montreal, July, 2013

wireless network models
Wireless Network Models
  • Purely graph-based models
    • Radio Broadcast (protocol) model
    • Dual Graph model

wireless network models1
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
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
so are these models realistic1
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
algorithm characteristics
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 characteristics1
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 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 theory1
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.
examples1
Examples
  • Low-level wireless communication
  • High-level wireless communication and computation.
  • Social insect colonies
  • Developing organisms
1 low level wireless communication
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
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
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
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
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
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
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
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
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.
summary needed work
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 f oundations
Concurrency theory foundations
  • General models based on interacting automata.
  • Must include time, discrete + continuous behavior, motion, probability.
  • Composition, abstraction.
  • Tailor for wireless systems.
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