A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
A sufficiently fast algorithm for finding close to optimal clique trees
Artificial Intelligence
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Pre-processing for Triangulation of Probabilistic Networks
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A New Lower Bound for Tree-Width Using Maximum Cardinality Search
SIAM Journal on Discrete Mathematics
A practical algorithm for finding optimal triangulations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Achievable sets, brambles, and sparse treewidth obstructions
Discrete Applied Mathematics
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Tree decomposition and discrete optimization problems: A survey
Cybernetics and Systems Analysis
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
Treewidth: A Useful Marker of Empirical Hardness in Quantified Boolean Logic Encodings
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Backtracking procedures for hypertree, hyperspread and connected hypertree decomposition of CSPs
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Duplicate avoidance in depth-first search with applications to treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Combining breadth-first and depth-first strategies in searching for treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Treewidth computations I. Upper bounds
Information and Computation
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Generation of tree decompositions by iterated local search
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
An Empirical Study of QBF Encodings: from Treewidth Estimation to Useful Preprocessing
Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
A local search algorithm for branchwidth
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Treewidth computations II. Lower bounds
Information and Computation
ISWC'11 Proceedings of the 10th international conference on The semantic web - Volume Part I
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Treewidth lower bounds with brambles
ESA'05 Proceedings of the 13th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Degree-Based treewidth lower bounds
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Ant colony optimization for tree decompositions
EvoCOP'10 Proceedings of the 10th European conference on Evolutionary Computation in Combinatorial Optimization
Exploiting the probability of observation for efficient bayesian network inference
Canadian AI'12 Proceedings of the 25th Canadian conference on Advances in Artificial Intelligence
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
All roads lead to Rome---New search methods for the optimal triangulation problem
International Journal of Approximate Reasoning
Evaluating tree-decomposition based algorithms for answer set programming
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Parameterized complexity results for exact bayesian network structure learning
Journal of Artificial Intelligence Research
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect elimination ordering of vertices of the graph. The algorithm uses novel pruning and propagation techniques which are derived from the theory of graph minors and graph isomorphism. We present a new algorithm called minor-min-width for computing a lower bound on treewidth that is used within the branch and bound algorithm and which improves over earlier available lower bounds. Empirical evaluation of QuickBB on randomly generated graphs and benchmarks in Graph Coloring and Bayesian Networks shows that it is consistently better than complete algorithms like Quick-Tree [Shoikhet and Geiger, 1997] in terms of cpu time. QuickBB also has good anytime performance, being able to generate a better upper bound on treewidth of some graphs whose optimal treewidth could not be computed up to now.