## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, March 22, 2012, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Ueli Peter

## How Random Is The Web?

Recently, it has been discovered that the web graph is highly compressible and can be stored in data structures which allow in-memory adjacency queries and need only $O(1)$ bits per edge. In this talk I present two such compression schemes. An intrinsic one that uses only the structure of the web graph and an extrinsic one that makes use of some additional coordinates (the URL of the web pages). I furthermore discuss a result by Chierichetti et. all. on the compressibility of a large class of models for the web graph. Finally, I will state an extrinsic compression scheme that stores random hyperbolic graphs in $O(n)$ bits with high probability.
Those three facts together indicate that the evolution of the web graph is driven by a mechanism that uses randomness mainly to equip the vertices with categories whose space is surprisingly well modeled by a uniform distribution on the hyperbolic space.

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