The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Bounded treewidth as a key to tractability of knowledge representation and reasoning
Artificial Intelligence
Tractable database design and datalog abduction through bounded treewidth
Information Systems
Treewidth computations I. Upper bounds
Information and Computation
Easy problems for grid-structured graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Monadic datalog over finite structures of bounded treewidth
ACM Transactions on Computational Logic (TOCL)
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
Approximation algorithms for the capacitated domination problem
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Querying Graphs in Protein-Protein Interactions Networks Using Feedback Vertex Set
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximation of minimum weight spanners for sparse graphs
Theoretical Computer Science
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A local search algorithm for branchwidth
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Parameterized complexity of coloring problems: Treewidth versus vertex cover
Theoretical Computer Science
Graphs of bounded treewidth can be canonized in AC1
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
An efficient partitioning oracle for bounded-treewidth graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
On Bounded-Degree Vertex Deletion parameterized by treewidth
Discrete Applied Mathematics
Treewidth of Erdős-Rényi random graphs, random intersection graphs, and scale-free random graphs
Discrete Applied Mathematics
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Multicut algorithms via tree decompositions
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Exploiting bounded treewidth with datalog (a survey)
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Parameterized maximum path coloring
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Efficient arbitrary and resolution proofs of unsatisfiability for restricted tree-width
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
On the tractability of query compilation and bounded treewidth
Proceedings of the 15th International Conference on Database Theory
On the directed Full Degree Spanning Tree problem
Discrete Optimization
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Preventing unraveling in social networks: the anchored k-core problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
European Journal of Combinatorics
D-flat: Declarative problem solving using tree decompositions and answer-set programming
Theory and Practice of Logic Programming
The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs
Journal of Combinatorial Optimization
Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
Parameterized complexity results for exact bayesian network structure learning
Journal of Artificial Intelligence Research
Data reduction for graph coloring problems
Information and Computation
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
Parameterized maximum path coloring
Theoretical Computer Science
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms. Starting from trees and series-parallel graphs, we introduce the concepts of treewidth and tree decompositions, and illustrate the technique with the Weighted Independent Set problem as an example. The paper surveys some of the latest developments, putting an emphasis on applicability, on algorithms that exploit tree decompositions, and on algorithms that determine or approximate treewidth and find tree decompositions with optimal or close to optimal treewidth. Directions for further research and suggestions for further reading are also given.