Speedup the optimization of maximal closure of a node-weighted directed acyclic graph

The maximal closure optimization problem of a node-weighted graph is a super class of the optimal monotonic Boolean function problem. It is known that the maximal closure optimization problem can be transformed to a min- s - t cut problem. This paper focuses on the complement problem of the maximal closure on a node-weighted directed acyclic graph, named optimal pruning of node-weighted directed acyclic graph (OPNWDAG). A variant of transformation is proposed and a framework of scheme is developed to speed up the solving time of the OPNWDAG. They also can be applied to solve the optimal monotonic Boolean function problem. The experiments show that the improvement is significant and the speedup of time complexity is O ( n 0.209 ) at least.