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

2. 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.

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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

9. 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?