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, 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)

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