The Complexity of MaxMin Length Triangulation
S\'andor P. Fekete
TL;DR
This paper proves that finding a MaxMin Length triangulation of a point set is NP-complete, resolving an open problem and indicating no efficient approximation algorithms exist unless P=NP.
Contribution
It establishes the NP-completeness of the MaxMin Length triangulation problem, a significant complexity result in computational geometry.
Findings
MaxMin Length triangulation is NP-complete
No polynomial-time approximation within any polynomial factor unless P=NP
Resolves an open problem from 1991
Abstract
In 1991, Edelsbrunner and Tan gave an O(n^2) algorithm for finding the MinMax Length triangulation of a set of points in the plane. In this paper we resolve one of the open problems stated in that paper, by showing that finding a MaxMin Length triangulation is an NP-complete problem. The proof implies that (unless P=NP), there is no polynomial-time approximation algorithm that can approximate the problem within any polynomial factor.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Complexity and Algorithms in Graphs