Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Learning Markov networks: maximum bounded tree-width graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Local Search and Placement of Meters in Networks
SIAM Journal on Computing
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
PAC-learning bounded tree-width graphical models
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Learning Factor Graphs in Polynomial Time and Sample Complexity
The Journal of Machine Learning Research
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Structure learning of Bayesian networks using constraints
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Finding a path is harder than finding a tree
Journal of Artificial Intelligence Research
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
On the power of structural decompositions of graph-based representations of constraint problems
Artificial Intelligence
Optimal Search on Clustered Structural Constraint for Learning Bayesian Network Structure
The Journal of Machine Learning Research
The Necessity of Bounded Treewidth for Efficient Inference in Bayesian Networks
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Learning bayesian network structure from massive datasets: the «sparse candidate« algorithm
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
A transformational characterization of equivalent Bayesian network structures
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
On the hardness of losing weight
ACM Transactions on Algorithms (TALG)
Approximating discrete probability distributions with dependence trees
IEEE Transactions on Information Theory
Learning optimal Bayesian networks using A* search
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Searching the k-change neighborhood for TSP is W[1]-hard
Operations Research Letters
The parameterized complexity of k-flip local search for SAT and MAX SAT
Discrete Optimization
Stable assignment with couples: Parameterized complexity and local search
Discrete Optimization
Parameterized Complexity
The Computer Journal Special Issue on Parameterized Complexity
The Computer Journal
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
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Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure. The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-based Bayesian network structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian network structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth, and in linear time if in addition the super-structure has bounded maximum degree. Furthermore, we show that if the directed super-structure is acyclic, then exact Bayesian network structure learning can be carried out in quadratic time. We complement these positive results with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Similarly, exact Bayesian network structure learning remains NP-hard for "almost acyclic" directed super-structures. Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).