David Eppstein – Publications

Improved mixing for the convex polygon triangulation flip walk.
D. Eppstein and D. Frishberg.
arXiv:2207.09972.
Proc. 50th EATCS International Colloquium on Automata, Languages, and Programming (ICALP 2023).
Leibniz International Proceedings in Informatics (LIPIcs) 261, 2023, pp. 56:1–56:17, doi:10.4230/LIPIcs.ICALP.2023.56.

The associahedron is a polytope whose vertices represent the triangulations of a convex polygon, and whose edges represent flips connecting one triangulation to another. We show that a random walk on the edges of this polytope rapidly converges to the uniform distribution on triangulations. However, we also show that the associahedron does not have constant expansion.

(Blog post: Flipping until you are lost)