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A Personal View of ToNC

A Personal View of ToNC. Christos H. Papadimitriou UC Berkeley “christos”. Why I work in ToNC. What else is there? Ideology meets competence Opportunity to do Game Theory Theory & experiment Cool playmates. Outline. “CToNC” Algorithms, games and networks

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A Personal View of ToNC

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  1. A Personal Viewof ToNC Christos H. Papadimitriou UC Berkeley “christos”

  2. Why I work in ToNC • What else is there? • Ideology meets competence • Opportunity to do Game Theory • Theory & experiment • Cool playmates ToNC, March 16 2006

  3. Outline • “CToNC” • Algorithms, games and networks • Vignette 1: Greedy routing • Vignette 2: The crowded center problem • Vignette 3: The economics of privacy ToNC, March 16 2006

  4. “CToNC” • Proving the last theorem • Think of it as a call to arms • Read the classics • With any luck, there will be a couple of them… ToNC, March 16 2006

  5. NetComp and Game Theory • Three prongs: • Computational mechanism design • Price of anarchy • Algorithms for equilibria • This is going well • (But may be at a juncture where infusion of new ideas is needed) ToNC, March 16 2006

  6. Routing in sensornets • IP envy • Use geography? • Greedy Routing: “Give the packet to your neighbor who is closest to the destination” ToNC, March 16 2006

  7. Greed can hurt you(~30% of the time…) to there “lake” gets stuck here packet from here remedy: face routing ToNC, March 16 2006

  8. Idea: fake coordinates greedy embedding: greedy is distance-decreasing ToNC, March 16 2006

  9. How do you find the fake coordinates? • By rubber bands! [PRRSS 03] • Is there always a “greedy embedding?” • Conjecture [PR05]: Every planar, 3-connected graph has a greedy embedding in the plane • (True for 3D) • Theorem [K06]: Every graph has a greedy embedding in the hyperbolic plane ToNC, March 16 2006

  10. ToNC, March 16 2006

  11. The burden of being central[KPPRS 06] Q: How do you relieve the center? ToNC, March 16 2006

  12. The burden of being central[KPPRS 06] Q: How do you relieve the center? A: By curveball routing Q: Optimal? ToNC, March 16 2006

  13. path lengths Optimum by LP max –c x Ax = 1 Bx t x 0 dual: min  + t  AT + BT  -c   0 limit on congestion, one constraint per “ring” “speed of light” as a function of r one variable per path, a continuum of variables… ToNC, March 16 2006

  14. Geometric optics! • Primal-dual: restricted primal is path of light under Snell’s law • When lights speed is(r) • Or simple iterative algorithm: “if congestion is too high at r, decrease speed of light (r)” • Still running… ToNC, March 16 2006

  15. The economics of privacy [KPR01] • Definition is elusive! • Personal data: IP bearing negative royalty • Opportunistic possession exploited • e.g., need for printer vs printer budget • Challenge: Calculate fair royalty • Methodology: Cooperative game theory ToNC, March 16 2006

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