Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
Quickly deciding minor-closed parameters in general graphs
European Journal of Combinatorics
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Contraction obstructions for treewidth
Journal of Combinatorial Theory Series B
Journal of Computer and System Sciences
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
The complexity of two graph orientation problems
Discrete Applied Mathematics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Computational study on bidimensionality theory based algorithm for longest path problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Survey: Subexponential parameterized algorithms
Computer Science Review
FPT results for signed domination
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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For several graph-theoretic parameters such as vertex cover and dominating set, it is known that if their sizes are bounded by k, then the treewidth of the graph is bounded by some function of k. This fact is used as the main tool for the design of several fixed-parameter algorithms on minor-closed graph classes such as planar graphs, single-crossing-minor-free graphs, and graphs of bounded genus. In this paper we examine whether similar bounds can be obtained for larger minor-closed graph classes and for general families of graph parameters, including all those for which such behavior has been reported so far. Given a graph parameter P, we say that a graph family $\mathcal{F}$ has the parameter-treewidth property for P if there is an increasing function t such that every graph $G\in\mathcal{F}$ has treewidth at most t(P(G)). We prove as our main result that, for a large family of graph parameters called contraction-bidimensional, a minor-closed graph family $\mathcal{F}$ has the parameter-treewidth property if $\mathcal{F}$ has bounded local treewidth. We also show "if and only if" for some graph parameters, and thus, this result is in some sense tight. In addition we show that, for a slightly smaller family of graph parameters called minor-bidimensional, all minor-closed graph families $\mathcal{F}$, excluding some fixed graphs, have the parameter-treewidth property. The contraction-bidimensional parameters include many domination and covering graph parameters such as vertex cover, feedback vertex set, dominating set, edge-dominating set, and q-dominating set (for fixed q). We use our theorems to develop new fixed-parameter algorithms in these contexts.