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Title: Improved Mixing for the Convex Polygon Triangulation Flip Walk
We prove that the well-studied triangulation flip walk on a convex point set mixes in time O(n³ log³ n), the first progress since McShine and Tetali’s O(n⁵ log n) bound in 1997. In the process we give lower and upper bounds of respectively Ω(1/(√n log n)) and O(1/√n) - asymptotically tight up to an O(log n) factor - for the expansion of the associahedron graph K_n. The upper bound recovers Molloy, Reed, and Steiger’s Ω(n^(3/2)) bound on the mixing time of the walk. To obtain these results, we introduce a framework consisting of a set of sufficient conditions under which a given Markov chain mixes rapidly. This framework is a purely combinatorial analogue that in some circumstances gives better results than the projection-restriction technique of Jerrum, Son, Tetali, and Vigoda. In particular, in addition to the result for triangulations, we show quasipolynomial mixing for the k-angulation flip walk on a convex point set, for fixed k ≥ 4.  more » « less
Award ID(s):
2212129
PAR ID:
10545642
Author(s) / Creator(s):
;
Editor(s):
Etessami, Kousha; Feige, Uriel; Puppis, Gabriele
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
261
ISSN:
1868-8969
ISBN:
978-3-95977-278-5
Page Range / eLocation ID:
261-261
Subject(s) / Keyword(s):
associahedron mixing time mcmc Markov chains triangulations quadrangulations k-angulations multicommodity flow projection-restriction Theory of computation → Approximation algorithms analysis
Format(s):
Medium: X Size: 17 pages; 1108039 bytes Other: application/pdf
Size(s):
17 pages 1108039 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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