A separator theorem for graphs of bounded genus
Journal of Algorithms
Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
Theoretical Computer Science
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Monotonicity in graph searching
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Finding minimal forbidden minors using a finite congruence
Proceedings of the 18th international colloquium on Automata, languages and programming
Better algorithms for the pathwidth and treewidth of graphs
Proceedings of the 18th international colloquium on Automata, languages and programming
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
DYNAMIC PROGRAMMING ON GRAPHS WITH BOUNDED TREEWIDTH
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Parametric Module Allocation on Partial k-Trees
IEEE Transactions on Computers
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The layout of virtual paths in ATM networks
IEEE/ACM Transactions on Networking (TON)
Counting H-colorings of partial k-trees
Theoretical Computer Science
Counting H-Colorings of Partial k-Trees
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
An Improved Algorithm for Finding Tree Decompositions of Small Width
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
Cutwidth II: algorithms for partial w-trees of bounded degree
Journal of Algorithms
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Header-size lower bounds for end-to-end communication in memoryless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking - Web dynamics
Online promise problems with online width metrics
Journal of Computer and System Sciences
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Traversing the machining graph
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph colouring with no large monochromatic components
Combinatorics, Probability and Computing
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
A nearly linear time algorithm for the half integral parity disjoint paths packing problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Efficient solution algorithms for factored MDPs
Journal of Artificial Intelligence Research
Constraint satisfaction with bounded treewidth revisited
Journal of Computer and System Sciences
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Treewidth computations I. Upper bounds
Information and Computation
Determining the smallest k such that G is k-outerplanar
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Shorter implicit representation for planar graphs and bounded treewidth graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Proceedings of the forty-second ACM symposium on Theory of computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On brambles, grid-like minors, and parameterized intractability of monadic second-order logic
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An (almost) linear time algorithm for odd cycles transversal
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Graphs of bounded treewidth can be canonized in AC1
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth 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
SIAM Journal on Discrete Mathematics
Constraint satisfaction with bounded treewidth revisited
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Approximate tree decompositions of planar graphs in linear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
Constraint optimization problems and bounded tree-width revisited
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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
Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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We show that for any fixed k, there is a linear-time algorithm which given a graph G either: (i) finds a cutset X of G with |X| ≤ k such that no component of G–X contains more than 3/4|G–X| vertices, or (ii) determines that for any set X of vertices of G with |X| ≤ k, there is a component of G–X which contains more than 2/3|G–X| vertices.This approximate separator algorithm can be used to develop and O(n log n algorithm for determining if G has a tree decomposition of width at most k (for fixed k) and finding such a tree decomposition if it exists.