关键词: 有界树宽, k-tree, Dandelion 编码, 条件偏好网络, 均匀性

Abstract: Aiming at the problem of high time complexity of Conditional Preference networks (CP-nets) graph model in reasoning computation, a Generating CP-nets with Bounded Tree Width based on Dandelion code (BTW-CP-nets Gen) algorithm was proposed. First, through the principle of bidirectional mapping between Dandelion code and tree structure with tree width k (k-tree), the decoding and encoding algorithms between Dandelion code and k-tree were derived to realize the one-to-one mapping between code and tree structure. Second, the k-tree was used to constrain the tree width of CP-nets structure, and the k-tree feature tree was used to obtain the directed acyclic graph structure of CP-nets. Finally, the bijection of discrete multi-valued functions was used to calculate the conditional preference table of each CP-nets node, and the dominant query test was executed to the generated bounded tree-width CP-nets. Theoretical analysis and experimental data show that, compared with the Pruffer code generating k-tree (Pruffer code) algorithm, BTW-CP-nets Gen algorithm has the running time on generating simple and complex structures reduced by 21.1% and 30.5% respectively,and the node traversal ratio of the graph model generated by BTW-CP-nets Gen in the dominant query is 18.48% and 29.03% higher on simple structure and complex structure respectively; the smaller the time consumed by BTW-CP-nets Gen algorithm, the higher the traversal node ratio of the dominant query. It can be seen that BTW-CP-nets Gen algorithm can effectively improve the algorithm efficiency in graph model reasoning.

Key words: bounded tree-width, k-tree, Dandelion code, Conditional Preference networks (CP-nets), uniformity