Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 22, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Lazar Todorovic

Size of Separators in GIRGs Depends on Underlying Geometry

This talk gives a brief overview of my recently completed Master Thesis. In Euclidean Geometric Inhomogeneous Random Graphs (GIRG), a model for real-networks recently presented by Bringmann, Keusch, and Lengler, each vertex is equipped with a weight and a position. The weights are drawn from a power-law distribution (with a fixed exponent $2 < \beta < 3$), while the positions are drawn uniformly from the $d$-dimensional torus $\mathbb{T}^d$. Then, the edge probability of two vertices is roughly polynomial in the product of their weights, and the inverse of their Euclidean distance. The Euclidean GIRG model has a wide range of interesting properties, such as a small diameter, small average distance, small separators, and a large clustering coefficient. The focus of the thesis lies on studying a variant of the GIRG model that uses minimum component distance (MCD) instead of Euclidean distance, but is otherwise defined in the same way as its Euclidean counterpart. The main result of the thesis is that the MCD model (for $d>1$) has no small (edge) separators, setting it apart from Euclidean GIRGs, and showing that the underlying geometry has a crucial influence on the separator property of GIRGs.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login