Analytical Foundations of Networked Computing

1
Analytical Foundations of Networked Computing

• Kirstie Bellman, Luiz DaSilva, Robert Kleinberg,
  Michael Mahoney, Amin Saberi, Ion Stoica, Eva
  Tardos,
• Shanghua Teng

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Overview of this presentation

• Define the problem
• Taxonomy, scope, dichotomies in ToNC.
• Mathematical modeling of networks and networked
  computation.
• Analytical paradigms for ToNC.
• ToNC problem domains not covered elsewhere.

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Understand and Model Different Kinds of Networks

• Examples of networks we should mean
• Internet, Sensor networks, DoD network GIG,
  mobile networks, P2P, pervasive computing
• Biological networks, Social Network??
• Same basic network model with few key parameters?
• develop a taxonomy
• what are the key parameters to consider?
• Do many basic properties depend on a few
  parameter?
• Properties and Issues
• open and evolving versus closed and stable
• mobile versus stable
• designed versus observed
• Controllability of the evolution
• impact and type of heterogeneity
• small word versus structured or mesh-like

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Analytical Paradigms for ToNC

• We need a holistic view of modeling all aspects
• network, traffic, interface.
• No need for perfection if network drops packets
  with small probability due to other reasons.
• Some applications need high reliability and
  precision other do not
• Analytical Paradigm like Smoothed Analysis
• Small randomness that captures some aspect of the
  uncertainty in the input.
• between worst-case and avg-case analysis
• uncertainty can come from
• numbers (traffic)
• network structure (small amount of randomness,
  such as neighbor selection in P2P
• can be added by the system (in timing)
• ordering arriving packets
• bit of noise can help avoid oscillation and other
  worst-case effects
• Other paradigms between average and worst case.
• GENI is an opportunity to test which of modes of
  analysis provides best results

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Challenges in Modeling Networks and Networked
Processes

• Model network self similarities
• maybe as a hierarchical network?
• some networks are only defined at this fuzzy
  level.
• social or geometric networks
• Rare events with catastrophic consequences need
  also be considered
• can be cumulative effect of "sub-threshold"
  events
• need a better "scenario generator" to reason
  about such events.
• Need to understand network diffusion effects to
  know what has catastrophic consequences.

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Networks controlled in a decentralized way

• Networks are no longer centralized
• Range of applications sensors, P2P, mobile
  networks, self-organizing system
• lack of knowledge
• modes of cooperation between nodes
• also related to selfishness and price
• Algorithmic theory of trust and reputation
  without assumptions about priors
• Additional issues for mobile networks
• How do solutions above solutions change with
  mobility of nodes

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Other Topics

• Geometry of Networked computing
• Develop theory of geometric random graphs
• small world routing
• taking advantage of low dimensionality of
  geometry
• effect of geometry not represented via the edges
  of the graph (like interference in wireless
  networks)
• Theory of random processes in networks
• graphs properties (such as power-low graphs)
• defense again cascading effects

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Theory of Information Networks

• Design communication paradigm for information
  networks in which you send modified or coded
  information.
• aggregating information in sensor networks
• Coding for multicast well understood, how about
  non-multicast applications
• How does coding effect needs to replicate files
• Error correcting codes in networks
• Information theory of networks of erasure channels

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What else should be included

• Molecular networks, biological networks, neural
  networks
• Research on network aspect such as propagation of
  information in these networks, structure network,
  and how effects functionality
• Characterizing expected quality depending on
  structural or other properties of network
• Other groups what else is missing?