On the Hyperbox – Hyperplane Intersection Problem

Finding the intersection between a hyperbox and a hyperplane can be computationally expensivespecially for high dimensional problems. Naive algorithms have an exponential complexity. Aborder node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperboxand the hyperplane. The algorithm proposed in this paper implements a systematic way to efficientlygenerate border nodes; given a border node, a subset of its incident edges is explored to determine one ormore intersections. This systematic exploration allows us to focus on the border region, discarding thetwo regions before and after the plane. Pruning those regions produces a computational cost linear onthe number of vertices of the hyperpolygon that represents the intersection