Using Recursive Decomposition to Construct Elimination Orders, Jointrees, and Dtrees
Darwiche has recently proposed a graphical model for driving conditioning algorithms, called a dtree, which specifies a recursive decomposition of a directed acyclic graph (DAG) into its families. A main property of a dtree is its width, and it was shown previously how to convert a DAG elimination order of width w into a dtree of width ≤ w. The importance of this conversion is that any algorithm for constructing low-width elimination orders can be directly used for constructing low-width dtrees. We propose in this paper a more direct method for constructing dtrees based on hypergraph partitioning. This new method turns out to be quite competitive with existing methods in minimizing width. We also present methods for converting a dtree of width w into elimination orders and jointrees of no greater width. This leads to a new class of algorithms for generating elimination orders and jointrees (via recursive decomposition).
KeywordsDirected Acyclic Graph Great Width Benchmark Circuit Elimination Order Left Subtree
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- 1.Charles J. Alpert and Andrew B. Kahng. Recent directions in netlist partitioning. Integration, the VLSI Journal, 19(1–81), 1995.Google Scholar
- 2.F. Beglez and H. Fujiwara. A neutral netlist of 10 combinational benchmark circuits and a target translator in FORTRAN. In Proceedings of the IEEE symposium on Circuits and Systems, 1985. http://www.cbl.ncsu.edu/www/CBLDocs/iscas85.html.
- 3.Adnan Darwiche. Compiling knowledge into decomposable negation normal form. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pages 284–289, 1999.Google Scholar
- 4.Adnan Darwiche. Utilizing device behavior in structure-based diagnosis. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pages 1096–1101, 1999.Google Scholar
- 5.Adnan Darwiche. Recursive conditioning. Artificial Intelligence, 126(1–2):5–41, February, 2001.Google Scholar
- 6.Adnan Darwiche and Mark Hopkins. Using recursive decomposition to construct elimination orders, jointrees and dtrees. Technical Report D-122, Computer Science Department, UCLA, Los Angeles, Ca 90095, 2001.Google Scholar
- 7.Rina Dechter. Bucket elimination: A unifying framework for probabilistic inference. In Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (UAI), pages 211–219, 1996.Google Scholar
- 8.Yousri El Fattah and Rina Dechter. An evaluation of structural paramters for probabilistic reasoning: Results on benchmark circuits. In Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (UAI), pages 244–251, 1996.Google Scholar
- 11.George Karypis, Rajat Aggarwal, Vipin Kumar, and Shashi Shekhar. Multilevel hypergraph partitioning: Applications in vlsi domain. IEEE Transactions on VLSI Systems, 1998.Google Scholar
- 12.George Karypis and Vipin Kumar. Hmetis: A hypergraph partitioning package. Available at http://www.cs.umn.edu/ karypis, 1998.
- 13.U. Kjaerulff. Triangulation of graphs—algorithms giving small total state space. Technical Report R-90-09, Department of Mathematics and Computer Science, University of Aalborg, Denmark, 1990.Google Scholar