Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**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)

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: 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