Monday, November 12, 2012
Freie Universität Berlin
Institut für Informatik
14195 Berlin Berlin
Lecture - 14:15
Imagine a group of interacting agents (eg, people, computers, birds, bacteria) subject to the attracting influence of the agents with which they communicate. Assume further that each agent is entitled to its own, distinct algorithm for deciding whom to listen to when.
The communication graph thus evolves endogenously in arbitrarily complex ways. We show that such an "influence system" is almost surely convergent if the communication is bidirectional and asymptotically periodic in general.
This suggests that social networks are more conducive to consensus than are older media like radio, tv, and newspapers. The proof introduces a technique of "algorithmic renormalization"likely to be of broader interest.
Colloquium - 16:00
Given a set of points, a covering path is a directed polygonal path that visits all the points. If no three points are collinear, any covering path (self-crossing or non-crossing) needs at least n/2 segments.
In both cases n-1 straight line segments obviously suffice. If the path can be self-crossing, then it is known that there exists a path with only n/2+O(n/log(n)) segments. The non-crossing case seems to be harder, we show an algorithm that finds a non-crossing covering path with at most (1-d)n segments, where d is a small constant.
joint work with Daniel Gerbner