ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Treewidth computations I. Upper bounds
Information and Computation
Theoretical Computer Science
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Approximate tree decompositions of planar graphs in linear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Towards fixed-parameter tractable algorithms for abstract argumentation
Artificial Intelligence
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
On the complexity of planning for agent teams and its implications for single agent planning
Artificial Intelligence
Sparsest cut on bounded treewidth graphs: algorithms and hardness results
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
Adiabatic quantum programming: minor embedding with hard faults
Quantum Information Processing
The complexity of optimal monotonic planning: the bad, the good, and the causal graph
Journal of Artificial Intelligence Research
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This paper presents algorithms whose input is an undirected graph, and whose output is a tree decomposition of width that approximates the optimal, the treewidth of that graph. The algorithms differ in their computation time and their approximation guarantees. The first algorithm works in polynomial-time and finds a factor-O(log OPT) approximation, where OPT is the treewidth of the graph. This is the first polynomial-time algorithm that approximates the optimal by a factor that does not depend on n, the number of nodes in the input graph. As a result, we get an algorithm for finding pathwidth within a factor of O(log OPT⋅log n) from the optimal. We also present algorithms that approximate the treewidth of a graph by constant factors of 3.66, 4, and 4.5, respectively and take time that is exponential in the treewidth. These are more efficient than previously known algorithms by an exponential factor, and are of practical interest. Finding triangulations of minimum treewidth for graphs is central to many problems in computer science. Real-world problems in artificial intelligence, VLSI design and databases are efficiently solvable if we have an efficient approximation algorithm for them. Many of those applications rely on weighted graphs. We extend our results to weighted graphs and weighted treewidth, showing similar approximation results for this more general notion. We report on experimental results confirming the effectiveness of our algorithms for large graphs associated with real-world problems.