Katharina Zweig IWR Heidel- berg Structure of the Real-World CV –Biochemistry –Theoretical Computer Science today –Biophysics/Statistical Physics today Research questions –What is the structure of the real-world –How does it interact with algorithms Current research statement: Theory needs experiments

Katharina Zweig IWR Heidel- berg Local Actions and Global Structure Given… …a system of egoistic agents that can connect to each other as they wish… …in an environment we have some control over… …what feedback should we give to the agents and… …what kind of behavior should we suggest… …such that local actions result in a wanted global structure?

Katharina Zweig IWR Heidel- berg Model Developer of system knows optimal global structure F(G(t)) Each user v determines usefulness of G(t) w.r.t. its own position in it: f(G(t),v)

Katharina Zweig IWR Heidel- berg Research Question How can we create the environment s.t. the individual actions to improve the structure coalesce into the optimal global structure.

Katharina Zweig IWR Heidel- berg First Question: How long can it take? Given some tree F(G) = diameter of tree Optimal structure: F(G) = 2 Egoistic evaluation: –f(G(t), v) = max distance of v to any other vertex (eccentricity) –f(G(t), v) = sum of distances (closeness)

Katharina Zweig IWR Heidel- berg Model Rewire one of your edges to one of your old neighbor‘s neighbors Keep old edge if egoistic function does not increase

Katharina Zweig IWR Heidel- berg Result Feedback of eccentricity will lead to exponential runtime; Feedback of closeness leads to polynomial runtime;

Katharina Zweig IWR Heidel- berg 2nd Question: Dynamic Change of Structure Almost all real-world networks have a strongly skewed degree distribution; This is helpful in so-called random failure scenarios This is harmful in so-called attack scenarios

Katharina Zweig IWR Heidel- berg Real-World Example Spanish Flu in the 1920 killed up to 50% of all 20 to 40 year old citizens Economic breakdowns

Katharina Zweig IWR Heidel- berg Stabilizing the Structure Global observer knows: –Scenario –Best network structure –What to feed back, what to recommend?

Katharina Zweig IWR Heidel- berg Two Recommendation Scenarios If an edge is lost, recommend building a new edge to –Any of all neighbors‘ neighbors u.a.r. –Each of all neighbors‘ neighbors with a prob. proportional to its degree

Katharina Zweig IWR Heidel- berg Result First induces approx. a random walk on the degree Second favors vertices with an above-average degree → fast spread of degrees

Katharina Zweig IWR Heidel- berg Open Questions 1st Question: –More general graph classes 2nd Question: –Velocity with which degree distribution spreads In General –Other combinations of global and egoistic functions