A subtree searching method with pruning for computing minimal m-Bézout number

It is a basic problem for homotopy continuation to minimize multi-homogeneous Bezout number of polynomial systems with multi-homogeneous structure. For a given polynomial system, different way of partitioning the variables produces different multi-homogeneous Bezout number. All possible variable partitions are regarded as a tree structure. We search in a subtree to find the optimal variable partition whose multi-homogeneous Bezout number is the smallest one. A pruned subtree searching method is proposed for saving the computational cost. Numerical tests with randomly generated examples show that these two methods are efficient.