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

Date and Time: Thursday, April 04, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Csaba D. Tóth (California State University Northridge)

Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning Trees

Let S be a set of n points in the plane in general position. The order type of S specifies, for every ordered triple, a positive or negative orientation; and the x-type (a.k.a. crossing type) of S specifies, for every unordered 4-tuple, whether they are in convex position. Geometric algorithms on S typically rely on primitives involving the order type or x-type (i.e., triples or 4-tuples). In this paper, we show that the x-type of S can be reconstructed from the compatible exchange graph G₁(S) of noncrossing spanning trees on S. This extends a recent result by Keller and Perles (2016), who proved that the x-type of S can be reconstructed from the exchange graph G₀(S) of noncrossing spanning trees, where G₁(S) is a subgraph of G₀(S). A crucial ingredient of our proof is a structure theorem on the maximal sets of pairwise noncrossing edges (MSNEs) between two components of a planar straight-line graph on the point set S. (Joint work with Marcos Oropeza)

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