Mixing times of Markov chains on 3-Orientations of Planar Triangulations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2012

Mixing times of Markov chains on 3-Orientations of Planar Triangulations


Given a planar triangulation, a 3-orientation is an orientation of the internal edges so all internal vertices have out-degree three. Each 3-orientation gives rise to a unique edge coloring known as a $\textit{Schnyder wood}$ that has proven useful for various computing and combinatorics applications. We consider natural Markov chains for sampling uniformly from the set of 3-orientations. First, we study a "triangle-reversing'' chain on the space of 3-orientations of a fixed triangulation that reverses the orientation of the edges around a triangle in each move. We show that (i) when restricted to planar triangulations of maximum degree six, the Markov chain is rapidly mixing, and (ii) there exists a triangulation with high degree on which this Markov chain mixes slowly. Next, we consider an "edge-flipping'' chain on the larger state space consisting of 3-orientations of all planar triangulations on a fixed number of vertices. It was also shown previously that this chain connects the state space and we prove that the chain is always rapidly mixing.
Fichier principal
Vignette du fichier
dmAQ0132.pdf (487 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01197229 , version 1 (11-09-2015)



Sarah Miracle, Dana Randall, Amanda Pascoe Streib, Prasad Tetali. Mixing times of Markov chains on 3-Orientations of Planar Triangulations. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.413-424, ⟨10.46298/dmtcs.3010⟩. ⟨hal-01197229⟩


90 View
556 Download



Gmail Facebook X LinkedIn More