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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Thursday, June 04, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Gabriel Nivasch (Tel Aviv Univ., Israel)

Encounters with the inverse Ackermann function

Given a point set X in R^d and a parameter epsilon<1, a "weak epsilon-net" for X is another point set N that intersects every convex set in R^d that contains an epsilon fraction of the points of X. The problem is to build such an N of minimal size. We show that, for cases in which the given set X lies in a so-called "convex curve" (a curve that is intersected at most d times by every hyperplane), there are upper and lower bounds for the size of N which are only slightly superlinear in 1/epsilon. The bounds have a complicated form involving the extremely slow-growing inverse Ackermann function. We obtain these results by reduction to a new combinatorial problem, interesting on its own right, which we call "stabbing interval chains". Amazingly, so-called Davenport-Schinzel sequences (an unrelated problem) are known to have almost-identical bounds. Inspired by our results on interval chains, we also improve the upper bounds for DS sequences.

Joint work with Noga Alon, Boris Bukh, Haim Kaplan, Jiří Matoušek, Micha Sharir, and Shakhar Smorodinsky.

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