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Information 2016, 7(1), 5; doi:10.3390/info7010005

The Treewidth of Induced Graphs of Conditional Preference Networks Is Small

School of Computer and Control Engineering, Yantai University, Yantai 264005, China
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Author to whom correspondence should be addressed.
Academic Editor: Willy Susilo
Received: 16 September 2015 / Revised: 1 February 2016 / Accepted: 2 February 2016 / Published: 14 February 2016
(This article belongs to the Section Information Theory and Methodology)
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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. View Full-Text
Keywords: conditional preference networks; induced graph; treewidth; bucket elimination; dominance queries conditional preference networks; induced graph; treewidth; bucket elimination; dominance queries
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liu, J.; Liu, J. The Treewidth of Induced Graphs of Conditional Preference Networks Is Small. Information 2016, 7, 5.

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