The neutral case for the min-max triangulation

Choosing the best triangulation of a point set is a question that has been debated for many years. Two of the most well known choices are the mitt-max criterion and the max-min criterion. The max-min triangulation criterion has received the most attention over the years because efficient algorithms have been developed for determining this triangulation. The ability to construct such efficient algorithms has been shown to be a result of the geometry of the neutralset for the max-min criterion. A point from the neutral set is formed from the special instance when the criterion is satisfied by more than one triangulation. For the max-min criterion, the neutral set is a circle. In this paper, we construct the neutral set for the mitt-max criterion. This construction is compared to that of the max-min triangulation and the results are analyzed in order to attain a better understanding of the nature of the min-max criterion.