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, May 31, 2018, 12:15 pm

Duration: 45 minutes

Location: OAT S15/S16/S17

Speaker: Manuel Broechin

Counting Triangulations in Subexponential Time

Given a set S of n points in the plane, a triangulation T of S is a maximal set of non-crossing segments with endpoints in S. In the talk I present an algorithm that computes the number of triangulations on a given set of n points in time n^{O(\sqrt(n)}. This result by Marx and Miltzow from 2016 significantly improves the previous best running time of O(2^n * n^2) by Alvarez and Seidel [SoCG 2013]. The main tool of the algorithm are canonical separators of size O(\sqrt{n}) of a triangulation. The definitions of the separators are based on the decomposition of triangulations into nested cactus layers.

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