AND/OR multi-valued decision diagrams (AOMDDs) for graphical models

Journal of Artificial Intelligence Research

Volumn 33, Issue , 2008, Pages 465-519

  Mateescu, Robert ^a   Dechter, Rina ^b   Marinescu, Radu ^c  

^a California Institute of Technology   (United States)

^b 5226 Donald Bren Hall   (United States)

^c UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY TREES; DECISION THEORY; GRAPHIC METHODS; MANY VALUED LOGICS; POLYNOMIALS; SEMANTICS;

BUCKET ELIMINATIONS; DECISION DIAGRAM; EXPERIMENTAL EVALUATION; FUNCTION DECOMPOSITION; MULTI-VALUED DECISION DIAGRAMS; ORDERED BINARY DECISION DIAGRAMS; PROBABILISTIC MODELS; SEARCH ALGORITHMS;

BINARY DECISION DIAGRAMS;

EID: 77952725880     PISSN: None     EISSN: 10769757     Source Type: Journal    
DOI: 10.1613/jair.2605     Document Type: Article

References (63)

1. Akers, S. (1978). Binary decision diagrams. IEEE Transactions on Computers, C-27(6), 509-516.
2. Allen, D., & Darwiche, A. (2003). New advances in inference by recursive conditioning. In Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI'03), pp. 2-10.
3. Bacchus, F., Dalmao, S., & Pitassi, T. (2003a). Algorithms and complexity results for #SAT and Bayesian inference. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), pp. 340-351.
4. Bacchus, F., Dalmao, S., & Pitassi, T. (2003b). Value elimination: Bayesian inference via backtracking search. In Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI'03), pp. 20-28.
5. Bahar, R., Frohm, E., Gaona, C., Hachtel, G., Macii, E., Pardo, A., & Somenzi, F. (1993). Algebraic decision diagrams and their applications. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD'93), pp. 188-191.
6. Bayardo, R., & Miranker, D. (1996). A complexity analysis of space-bound learning algorithms for the constraint satisfaction problem. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI'96), pp. 298-304.
7. Bayardo, R. J., & Schrag, R. C. (1997). Using CSP look-back techniques to solve real world SAT instances. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI'97), pp. 203-208.
8. Bertacco, V., & Damiani, M. (1997). The disjunctive decomposition of logic functions. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD'97), pp. 78-82.
9. Bodlaender, H. L., & Gilbert, J. R. (1991). Approximating treewidth, pathwidth and minimum elimination tree height. Tech. rep., Utrecht University.
10. Bryant, R. E. (1986). Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, 35, 677-691.
11. Cadoli, M., & Donini, F. M. (1997). A survey on knowledge compilation. AI Communications, 10(3-4), 137-150.
12. Chavira, M., & Darwiche, A. (2005). Compiling Bayesian networks with local structure. In Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI' 05), pp. 1306-1312.
13. Chavira, M., & Darwiche, A. (2007). Compiling Bayesian networks using variable elimination. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI' 07), pp. 2443-2449.
14. Chavira, M., Darwiche, A., & Jaeger, M. (2006). Compiling relational Bayesian networks for exact inference. International Journal of Approximate Reasoning, 42(1-2), 4-20.
15. Clarke, E., Grumberg, O., & Peled, D. (1999). Model Checking. MIT Press.
16. Collin, Z., Dechter, R., & Katz, S. (1991). On the feasibility of distributed constraint satisfaction. In Proceedings of the Twelfth International Conference of Artificial Intelligence (IJCAI'91), pp. 318-324.
17. Collin, Z., Dechter, R., & Katz, S. (1999). Self-stabilizing distributed constraint satisfaction. The Chicago Journal of Theoretical Computer Science, 115, special issue on self-stabilization.
18. Darwiche, A. (2001). Recursive conditioning. Artificial Intelligence, 125(1-2), 5-41.
19. Darwiche, A. (2002). A logical approach to factoring belief networks. In Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR'02), pp. 409-420.
20. Darwiche, A., & Marquis, P. (2002). A knowledge compilation map. Journal of Artificial Intelligence Research (JAIR), 17, 229-264.
21. Dechter, R. (1992). Constraint networks. Encyclopedia of Artificial Intelligence, 276-285.
22. Dechter, R. (1999). Bucket elimination: A unifying framework for reasoning. Artificial Intelligence, 113, 41-85.
23. Dechter, R., & Mateescu, R. (2007). AND/OR search spaces for graphical models. Artificial Intelligence, 171(2-3), 73-106.
24. Dechter, R., & Mateescu, R. (2004a). Mixtures of deterministic- probabilistic networks and their AND/OR search space. In Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI'04), pp. 120-129.
25. Dechter, R., & Mateescu, R. (2004b). The impact of AND/OR search spaces on constraint satisfaction and counting. In Proceedings of the Tenth International Conference on Principles and Practice of Constraint Programming (CP'04), pp. 731-736.
26. Dechter, R., & Pearl, J. (1989). Tree clustering for constraint networks. Artificial Intelligence, 38, 353-366.
27. Drechsler, R., Becker, B., & Ruppertz, S. (1996). K*BMDs: A new data structure for verification. In Proceedings of the 1996 European conference on Design and Test (ED&TC'96), pp. 2-8.
28. Drechsler, R., & Sieling, D. (2001). Binary decision diagrams in theory and practice. International Journal on Software Tools for Technology Transfer (STTT), 3(2), 112-136.
29. Fargier, H., & Marquis, P. (2006). On the use of partially ordered decision graphs in knowledge compilation and quantified boolean formulae. In Proceedings of The Twenty-First National Conference on Artificial Intelligence (AAAI'06), pp. 42-47.
30. Fargier, H., & Marquis, P. (2007). On valued negation normal form formulas. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07), pp. 360-365.
31. Fargier, H., & Vilarem, M. (2004). Compiling CSPs into tree-driven automata for interactive solving. Constraints, 9(4), 263-287.
32. Fishburn, P. C. (1970). Utility Theory for Decision Making. Wiley, NewYork.
33. Freuder, E. C., & Quinn, M. J. (1985). Taking advantage of stable sets of variables in constraint satisfaction problems. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI'85), pp. 1076-1078.
34. Freuder, E. C., & Quinn, M. J. (1987). The use of lineal spanning trees to represent constraint satisfaction problems. Tech. rep. 87-41, University of New Hampshire, Durham.
35. Huang, J., & Darwiche, A. (2005a). On compiling system models for faster and more scalable diagnosis. In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI'05), pp. 300-306.
36. Huang, J., & Darwiche, A. (2005b). DPLL with a trace: From SAT to knowledge compilation. In Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI'05), pp. 156-162.
37. Jaeger, M. (2004). Probabilistic decision graphs - combining verification and AI techniques for probabilistic inference. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 19-42.
38. Kask, K., Dechter, R., Larrosa, J., & Dechter, A. (2005). Unifying cluster-tree decompositions for reasoning in graphical models. Artificial Intelligence, 166 (1-2), 165-193.
39. Kjæaerulff, U. (1990). Triangulation of graph-based algorithms giving small total state space. Tech. rep., University of Aalborg, Denmark.
40. Korf, R., & Felner, A. (2002). Disjoint pattern database heuristics. Artificial Intelligence, 134(1-2), 9-22.
41. Lai, Y.-T., & Sastry, S. (1992). Edge-valued binary decision for multi-level hierarchical verification. In Proceedings of the Twenty Nineth Design Automation Conference, pp. 608-613.
42. Larrosa, J., Meseguer, P., & Sanchez, M. (2002). Pseudo-tree search with soft constraints. In Proceedings of the European Conference on Artificial Intelligence (ECAI'02), pp. 131-135.
43. Lee, C. (1959). Representation of switching circuits by binary-decision programs. Bell System Technical Journal, 38, 985-999.
44. Mateescu, R., & Dechter, R. (2005). The relationship between AND/OR search and variable elimination. In Proceedings of the Twenty First Conference on Uncertainty in Artificial Intelligence (UAI'05), pp. 380-387.
45. Mateescu, R., & Dechter, R. (2007). AND/OR multi-valued decision diagrams (AOMDDs) for weighted graphical models. In Proceedings of the Twenty Third Conference on Uncertainty in Artificial Intelligence (UAI'07), pp. 276-284.
46. McAllester, D., Collins, M., & Pereira, F. (2004). Case-factor diagrams for structured probabilistic modeling. In Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI'04), pp. 382-391.
47. McMillan, K. L. (1993). Symbolic Model Checking. Kluwer Academic.
48. McMillan, K. L. (1994). Hierarchical representation of discrete functions with application to model checking. In Computer Aided Verification, pp. 41-54.
49. Modi, P. J., Shen, W., Tambe, M., & Yokoo, M. (2005). ADOPT: asynchronous distributed constraint optimization with quality guarantees. Artificial Intelligence, 161, 149-180.
50. Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., & Malik, S. (2001). Chaff: Engineering an efficient SAT solver. In Proceedings of the Thirty Eighth Design Automation Conference, pp. 530-535.
51. Nilsson, N. J. (1980). Principles of Artificial Intelligence. Tioga, Palo Alto, CA.
52. Palacios, H., Bonet, B., Darwiche, A., & Geffner, H. (2005). Pruning conformant plans by counting models on compiled d-DNNF representations. In Proceedings of the 15th International Conference on Planning and Scheduling (ICAPS'05), pp. 141-150.
53. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.
54. Sang, T., Bacchus, F., Beame, P., Kautz, H., & Pitassi, T. (2004). Combining component caching and clause learning for effective model counting. In Proceedings of the Seventh International Conference on Theory and Applications of Satisfiability Testing (SAT'04).
55. Sanner, S., & McAllester, D. (2005). Affine algebraic decision diagrams (AADDs) and their application to structured probabilistic inference. In Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI'05), pp. 1384-1390.
56. Selman, B., & Kautz, H. (1996). Knowledge compilation and theory approximation. Journal of the ACM, 43(2), 193-224.
57. Shenoy, P. (1992). Valuation-based systems for Bayesian decision analysis. Operations Research, 40, 463-484.
58. Srinivasan, A., Kam, T., Malik, S., & Brayton, R. K. (1990). Algorithms for discrete function manipulation. In International conference on CAD, pp. 92-95.
59. Tafertshofer, P., & Pedram, M. (1997). Factored edge-valued binary decision diagrams. Formal Methods in System Design, 10(2-3), 243-270.
60. Terrioux, C., & J́egou, P. (2003a). Bounded backtracking for the valued constraint satisfaction problems. In Proceedings of the Ninth International Conference on Principles and Practice of Constraint Programming (CP'03), pp. 709-723.
61. Terrioux, C., & Jégou, P. (2003b). Hybrid backtracking bounded by tree-decomposition of constraint networks. Artificial Intelligence, 146, 43-75.
62. Wilson, N. (2005). Decision diagrams for the computation of semiring valuations. In Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI'05), pp.331-336.
63. Zuzek, A., Drechsler, R., & Thornton, M. (2000). Boolean function representation and spectral characterization using AND/OR graphs. Integration, The VLSI journal, 29, 101-116.