Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
On the complexity of dynamic programming for sequencing problems with precedence constraints
Annals of Operations Research
Dynamic Programming Treatment of the Travelling Salesman Problem
Journal of the ACM (JACM)
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Exact Bayesian Structure Discovery in Bayesian Networks
The Journal of Machine Learning Research
Large-Sample Learning of Bayesian Networks is NP-Hard
The Journal of Machine Learning Research
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
The Journal of Machine Learning Research
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact Algorithms for Exact Satisfiability and Number of Perfect Matchings
Algorithmica - Parameterized and Exact Algorithms
Structure learning of Bayesian networks using constraints
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Responsibility and blame: a structural-model approach
Journal of Artificial Intelligence Research
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Exact structure discovery in Bayesian networks with less space
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Globally optimal structure learning of Bayesian networks from data
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part I
Efficient Structure Learning of Bayesian Networks using Constraints
The Journal of Machine Learning Research
Parallel Algorithm for Learning Optimal Bayesian Network Structure
The Journal of Machine Learning Research
Parent assignment is hard for the MDL, AIC, and NML costs
COLT'06 Proceedings of the 19th annual conference on Learning Theory
A Note on Exact Algorithms for Vertex Ordering Problems on Graphs
Theory of Computing Systems
Learning optimal Bayesian networks using A* search
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
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We consider the problem of finding a directed acyclic graph (DAG) that optimizes a decomposable Bayesian network score. While in a favorable case an optimal DAG can be found in polynomial time, in the worst case the fastest known algorithms rely on dynamic programming across the node subsets, taking time and space 2n, to within a factor polynomial in the number of nodes n. In practice, these algorithms are feasible to networks of at most around 30 nodes, mainly due to the large space requirement. Here, we generalize the dynamic programming approach to enhance its feasibility in three dimensions: first, the user may trade space against time; second, the proposed algorithms easily and efficiently parallelize onto thousands of processors; third, the algorithms can exploit any prior knowledge about the precedence relation on the nodes. Underlying all these results is the key observation that, given a partial order P on the nodes, an optimal DAG compatible with P can be found in time and space roughly proportional to the number of ideals of P, which can be significantly less than 2n. Considering sufficiently many carefully chosen partial orders guarantees that a globally optimal DAG will be found. Aside from the generic scheme, we present and analyze concrete tradeoff schemes based on parallel bucket orders.