NP is as easy as detecting unique solutions
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
IEEE Transactions on Systems, Man and Cybernetics - Special issue on artificial intelligence
Operations Research
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
Introduction to algorithms
Approximating probabilistic inference in Bayesian belief networks is NP-hard
Artificial Intelligence
Probabilistic Horn abduction and Bayesian networks
Artificial Intelligence
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
Local conditioning in Bayesian networks
Artificial Intelligence
Approximating MAPs for belief networks is NP-hard and other theorems
Artificial Intelligence
Graph orientations with no sink and an approximation for a hard case of #SAT
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
An O(|V|2) algorithm for single connectedness
Information Processing Letters
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Conditioning algorithms for exact and approximate inference in causal networks
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Approximate belief updating in max-2-connected Bayes networks is NP-hard
Artificial Intelligence
Journal of Artificial Intelligence Research
A learning-based algorithm selection meta-reasoner for the real-time MPE problem
AI'04 Proceedings of the 17th Australian joint conference on Advances in Artificial Intelligence
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Directed-path (DP) singly-connected Bayesian networks are an interesting special case that, in particular, includes both polytrees and two-level networks. We analyze the computational complexity of these networks. The prediction problem is shown to be easy, as standard message passing can perform correct updating. However, diagnostic reasoning is hard even for DP singly-connected networks. In addition, finding the most-probable explanation (MPE) is hard, even without evidence. Finally, complexity of nearly DP singly-connected networks is analyzed.