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: Tuesday, November 23, 2021, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Saeed Ilchi

Perfect Matching in the Plane with Small Detour

Consider a perfect matching M on a point set of size 2n in the plane. A point p is a k-detour for M if for any matched pair of points (a,b), we have |a - p| + |p - b| ≤ k|a - b|. For any point set, we show that there is always a matching with a 2/sqrt(3)-detour. This is tight due to a simple lower bound that can be obtained from equilateral triangles. The best previous bound was sqrt(2).

This is a joint work with Bernd Gärtner, Yoshio Okamoto, Patrick Schnider, and Tim Taubner.

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