Abstract
Conditional preference networks (CP-nets) are recently an emerging topic as a graphical model for compactly representing ordinal conditional preference relations on multi-attribute domains. As we know, the treewidth, which can decrease the solving complexity for many intractability problems, is exactly a fundamental property of a graph. Therefore, we can utilize treewidth to solve some reasoning tasks on induced graphs, such as the dominance queries on the CP-nets in the future. In this paper, we present an efficient algorithm for computing the treewidth of induced graphs of CP-nets; what we need is to make an assumption that the induced graph of a CP-net has been given. Then, we can leverage the Bucket Elimination technique to solve treewidth within polynomial time. At last, it is revealed that by our experiment, the treewidth of induced graphs of CP-nets is much smaller with regard to the number of vertices. For example, for an induced graph of CP-net with 1024 vertices, its treewidth is only 10. As far as we know, this is the first time, using the Bucket Elimination, to compute the treewidth of an induced graph of a CP-net. This approach for solving the treewidth may lay a good foundation for efficiently solving dominance queries on CP-nets in the future.
Highlights
Conditional preference networks (CP-nets) [1,2] have permeated our daily life as a specific graphical model
We explore the treewidth problem about the induced graphs of CP-nets— as far as we know, there is no literature availlable to study the treewidth characterization of induced graphs of CP-nets
We find that the treewidth of induced graphs of CP-nets is very small; this interesting discovery may lay the foundation for designing an algorithm for solving tractable reasoning tasks, such as dominance queries, in the future
Summary
Conditional preference networks (CP-nets) [1,2] have permeated our daily life as a specific graphical model. CP-nets express a user’s preference for evening dress, we work out the treewidth of its induced graph. Some operations, such as dominance queries [1], can be solved quickly. We design a more efficient algorithm to solve the treewidth of induced graphs of CP-nets utilizing a Bucket Elimination approach; this approach uses the randomness characteristics of input order to speed search. We find that the treewidth of induced graphs of CP-nets is very small; this interesting discovery may lay the foundation for designing an algorithm for solving tractable reasoning tasks, such as dominance queries, in the future.
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