A fast algorithm for computing irreducible triangulations of closed surfaces in $E^d$

TL;DR

This paper presents a fast algorithm for computing irreducible triangulations of closed surfaces in Euclidean space, improving efficiency especially for surfaces with positive genus.

Contribution

The authors introduce a new algorithm that reduces the computational complexity for irreducible triangulations, especially for surfaces with positive genus, while maintaining linear space.

Findings

Algorithm runs in O(g^2+gn) time for positive genus surfaces

Algorithm runs in linear time for genus zero surfaces

Memory usage is linear in the number of triangles

Abstract

We give a fast algorithm for computing an irreducible triangulation $T^\prime$ of an oriented, connected, boundaryless, and compact surface $S$ in $E^d$ from any given triangulation $T$ of $S$. If the genus $g$ of $S$ is positive, then our algorithm takes $O(g^2+gn)$ time to obtain $T^\prime$, where $n$ is the number of triangles of $T$. Otherwise, $T^\prime$ is obtained in linear time in $n$. While the latter upper bound is optimal, the former upper bound improves upon the currently best known upper bound by a $(\lg n / g)$ factor. In both cases, the memory space required by our algorithm is in ${\Theta}(n)$.