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Insights into Algorithms, Games, and Networks - A Personal Perspective by Christos H. Papadimitriou

Delve into the realm of algorithms, games, and networks through Christos H. Papadimitriou's personal view, exploring concepts like greedy routing, computational mechanism design, and the economics of privacy. Discover the intersection of ideology and competence, the opportunities in game theory, and the fusion of theory with experimentation. Join this journey of knowledge and innovation, where theoretical insights meet real-world applications.

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Insights into Algorithms, Games, and Networks - A Personal Perspective by Christos H. Papadimitriou

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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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