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, August 20, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Torsten Mütze (University of Warwick)

On the central levels problem

The central levels problem asserts that the subgraph of the (2m+1)-dimensional hypercube induced by all bitstrings with at least m+1-k many 1s and at most m+k many 1s, i.e., the vertices in the middle 2k levels, has a Hamilton cycle for any m≥1 and 1≤k≤m+1. This problem was raised independently by Buck and Wiedemann, Savage, Gregor and Škrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case k=1, and classical binary Gray codes, namely the case k=m+1.
In this talk I present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of k consecutive levels in the n-dimensional hypercube for any n≥1 and 1≤k≤n+1. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the n-dimensional hypercube, n≥2, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code (here is a link to experiment with this algorithm:

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