Optimality and integer programming formulations of triangulations in general dimension

The properties of triangulations in two and three dimensions are computationally investigated by using integer programming (IP). Three IP formulations of triangulations are introduced, two based on the stable set problem, and the other based on the set partitioning problem. Some properties that are interesting from a theoretical or practical point of view are considered as objective functions for IP. Finally, some computational results are given. This approach allows three-dimensional triangulations to be treated in a flexible and efficient way, and has led to the discovery of some interesting properties of three-dimensional triangulations.