Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Ka,k minors in graphs of bounded tree-width
Journal of Combinatorial Theory Series B
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Parameterized Complexity of Counting Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
The Dominating Set Problem Is Fixed Parameter Tractable for Graphs of Bounded Genus
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Dimension Reduction in the \ell _1 Norm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences
Graph Theory With Applications
Graph Theory With Applications
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Genus characterizes the complexity of graph problems: some tight results
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
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
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
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We introduce a new framework for designing fixed-parameter algorithms with subexponential running time---2O(√k)nO(1). Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and covering problems such as vertex cover, feedback vertex set, minimum maximal matching, dominating set, edge dominating set, clique-transversal set, and many others restricted to bounded-genus graphs. Furthermore, it is fairly straightforward to prove that a problem is bidimensional. In particular, our framework includes as special cases all previously known problems to have such subexponential algorithms. Previously, these algorithms applied to planar graphs, single-crossing-minor-free graphs, and map graphs; we extend these results to apply to bounded-genus graphs as well. In a parallel development of combinatorial results, we establish an upper bound on the treewidth (or branchwidth) of a bounded-genus graph that excludes some planar graph H as a minor. This bound depends linearly on the size |V (H)| of the excluded graph H and the genus g(G) of the graph G, and applies and extends the graphminors work of Robertson & Seymour.Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. In particular, this general category of graphs includes planar graphs, bounded-genus graphs, single-crossing-minor-free graphs, and any class of graphs that is closed under taking minors. Specifically, the running time is 2O(√k)nh, where h is a constant depending only on H, which is polynomial for k = O(log2n). We introduce a general approach for developing algorithms on H-minor-free graphs, based on structural results about H-minor-free graphs at the heart of Robertson & Seymour's graph-minors work. We believe this approach opens the way to further development for problems on H-minor-free graphs.