刘思光, 欧阳丹彤, 王艺源, 贾凤雨, 张立明. 结合SE-Tree结构特征的极小碰集求解算法[J]. 计算机研究与发展, 2016, 53(11): 2556-2566.
 引用本文: 刘思光, 欧阳丹彤, 王艺源, 贾凤雨, 张立明. 结合SE-Tree结构特征的极小碰集求解算法[J]. 计算机研究与发展, 2016, 53(11): 2556-2566.
Liu Siguang, Ouyang Dantong, Wang Yiyuan, Jia Fengyu, Zhang Liming. Algorithm of Computing Minimal Hitting Set Based on the Structural Feature of SE-Tree[J]. Journal of Computer Research and Development, 2016, 53(11): 2556-2566.
 Citation: Liu Siguang, Ouyang Dantong, Wang Yiyuan, Jia Fengyu, Zhang Liming. Algorithm of Computing Minimal Hitting Set Based on the Structural Feature of SE-Tree[J]. Journal of Computer Research and Development, 2016, 53(11): 2556-2566.

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

• 摘要: 在结合SE-Tree计算集合簇极小碰集的过程中,现有算法会对大量不会产生碰集的冗余节点进行访问.这无疑将影响算法的效率,冗余节点比例越高,影响越大.通过对SE-Tree中叶节点的特殊性质的分析,并结合现有碰集算法有解空间中冗余节点的特征,提出非解冗余节点概念.在对SE-Tree的结构特征进行深入分析基础上,根据非碰集的子集也不是碰集的特点,提出辅助剪枝的概念,通过在剪枝树上设置剪枝判定节点,减少对极小碰集求解过程中无解空间的访问;针对较大规模问题,还提出结合多级辅助剪枝树的极小碰集求解算法,进而较大程度地减少对非解冗余节点的访问;根据多级辅助剪枝树及SE-Tree的结构特征,给出提前终止算法的判定条件,并证明了此算法的正确性.实验结果表明:与效率较高的Boolean算法相比,该算法高效且易于实现,尤其是对规模较大的问题,效率能提升1个数量级.

Abstract: 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.

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