A Personal View of To NC Christos H

A Personal View of To. NC Christos H. Papadimitriou UC Berkeley “christos” To. NC, March 16 2006

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

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

“CTo. NC” • • 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… To. NC, March 16 2006 4

Net. Comp 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) To. NC, March 16 2006 5

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

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

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

How do you find the fake coordinates? • By rubber bands! [PRRSS 03] • Is there always a “greedy embedding? ” • Conjecture [PR 05]: Every planar, 3 -connected graph has a greedy embedding in the plane • (True for 3 D) • Theorem [K 06]: Every graph has a greedy embedding in the hyperbolic plane To. NC, March 16 2006 9

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

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

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

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… To. NC, March 16 2006 14

The economics of privacy [KPR 01] • • • 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 To. NC, March 16 2006 15