The Treewidth of Induced Graphs of Conditional Preference Networks Is Small

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.

Development and investigation of methods of graphic-functional modeling of distributed systems

“…The paper [14] operates with the use of induced graphs in the problems of designing systems reproduced by the networks of conditional preference (CP-networks). In the paper [14], a method for calculating the triple sequence of the induced graph of the CP-network is proposed.…”

“…The paper [14] operates with the use of induced graphs in the problems of designing systems reproduced by the networks of conditional preference (CP-networks). In the paper [14], a method for calculating the triple sequence of the induced graph of the CP-network is proposed. As a result, it is possible to reduce the dimension of graphic models (in terms of the number of vertices and edges) for reproduction of technological systems and objects of arbitrary purpose.…”

“…Either way, it is necessary to generalize the methods, models and means of graph-analytical modeling of distributed technological systems and objects, set forth in the writings [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In the aspect of the application of these categories in order to research the work and automated design of information management systems, one can distinguish such general limitations and disadvantages:…”

Cutting Cycles of Conditional Preference Networks with Feedback Set Approach

“…In [ 12 ], Liu et al utilize treewidth which can decrease the solving complexity to solve some reasoning tasks on induced graphs, such as the dominance queries on the CP-nets in the future. And they present an efficient algorithm for computing the treewidth of induced graphs of CP-nets.…”