Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 5 (2015), 763-770.

Expected maximum vertex valence in pairs of polygonal triangulations

Timothy Chu and Sean Cleary

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Abstract

Edge-flip distance between triangulations of polygons is equivalent to rotation distance between rooted binary trees. Both distances measure the extent of similarity of configurations. There are no known polynomial-time algorithms for computing edge-flip distance. The best known exact universal upper bounds on rotation distance arise from measuring the maximum total valence of a vertex in the corresponding triangulation pair obtained by a duality construction. Here we describe some properties of the distribution of maximum vertex valences of pairs of triangulations related to such upper bounds.

Article information

Source
Involve, Volume 8, Number 5 (2015), 763-770.

Dates
Received: 6 March 2014
Revised: 17 October 2014
Accepted: 22 November 2014
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370947

Digital Object Identifier
doi:10.2140/involve.2015.8.763

Mathematical Reviews number (MathSciNet)
MR3404656

Zentralblatt MATH identifier
1328.51009

Subjects
Primary: 05C05: Trees 68P05: Data structures

Keywords
random binary trees

Citation

Chu, Timothy; Cleary, Sean. Expected maximum vertex valence in pairs of polygonal triangulations. Involve 8 (2015), no. 5, 763--770. doi:10.2140/involve.2015.8.763. https://projecteuclid.org/euclid.involve/1511370947


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