Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 14, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Fabian Kuhn (Microsoft Research Silicon Valley, California)

Reconstructing Approximate Tree Metrics

If any four points of a metric space can be isometrically embedded into a tree, the whole metric can be isometrically embedded into a tree. This is called the four-point condition and a metric space satisfying the four-point condition is called a tree metric. We introduce a parameter eps and consider a natural relaxation of the four-point condition such that tree metrics have eps=0 and such that any metric space has an eps in [0,1]. We call our relaxation the eps-four-point condition. We show that there are constants c_1 and c_2 such that any metric space which satisfies the eps-four-point condition can be embedded into a tree with distortion (1+eps)^(c_1*log n) and such that for every eps in [0,1], there is a metric space satisfying the eps-four-point condition which does not embed into a tree with distortion less than (1+eps)^(c_2*log n). The lower bound implies that for every eps in [0,1], there is a metric space such that any set of four points can be embedded into a tree with distortion 1+eps but where any tree embedding has distortion at least (1+eps)^(c_2*log n).

Joint work with Ittai Abraham, Dahlia Malkhi, and Kunal Talwar.

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

Previous talks by year:   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