Algorithm of Computing Minimal Hitting Set Based on the Structural Feature of SE-Tree

During the process of computing minimal hitting set (MHS) by SE-Tree, it will generate many redundant nodes that cannot be pruned by current SE-Tree based algorithms, which affects the efficiency of these algorithms, i.e., the higher the ratio of redundant nodes is, the greater likely the impact of algorithms has. In this paper, firstly we introduce the definition of redundant nodes by analyzing the characteristic of leaf-node in SE-Tree and the redundant nodes in solution space in existent algorithms. Secondly, on the basis of analyzing the structural feature of SE-Tree and the theory that the subset of non-hitting set is non-hitting set, we propose the concept of assistant pruning tree. Specially, the decision nodes are added into the assistant pruning tree, which can largely reduce the visit of non-solution space. Furthermore, in order to decrease the visit of non-solution space when computing larger problem as much as possible, the algorithm of computing minimal hitting set combining with multi-level assistant pruning tree is proposed. Finally, we set a reasonable termination condition to make our algorithm stop without losing correct solution as early as possible, and then prove its correctness. Results show that the proposed algorithm is easily implemented and efficient. Moreover, our algorithm significantly outperforms a state-of-the-art minimal hitting set algorithm Boolean, even up to one order of magnitude for some instances.