Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Resolution versus Search: Two Strategies for SAT
Journal of Automated Reasoning
Optimizing exact genetic linkage computations
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Constraint Processing
Cycle-cutset sampling for Bayesian networks
AI'03 Proceedings of the 16th Canadian society for computational studies of intelligence conference on Advances in artificial intelligence
Random algorithms for the loop cutset problem
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
A sufficiently fast algorithm for finding close to optimal junction trees
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
An empirical study of w-cutset sampling for bayesian networks
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Cutset sampling for Bayesian networks
Journal of Artificial Intelligence Research
M-DPOP: faithful distributed implementation of efficient social choice problems
Journal of Artificial Intelligence Research
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Matched formulas and backdoor sets
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Structural relaxations by variable renaming and their compilation for solving MinCostSAT
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
SampleSearch: Importance sampling in presence of determinism
Artificial Intelligence
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The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of the network is singly-connected and therefore can be solved by linear propagation algorithms. A w-cutset is a generalization of a cycle-cutset defined as a subset of nodes such that the subgraph with cutset nodes removed has induced-width of w or less. In this paper we address the problem of finding a minimal w-cutset in a graph. We relate the problem to that of finding the minimal w-cutset of a tree-decomposition. The latter can be mapped to the well-known set multi-cover problem. This relationship yields a proof of NP-completeness on one hand and a greedy algorithm for finding a w-cutset of a tree decomposition on the other. Empirical evaluation of the algorithms is presented.