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
Graph minors. XI.: circuits on a surface
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Graph minors. XII: distance on a surface
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
Journal of Combinatorial Theory Series B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
-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
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
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
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
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
The dominating set problem is fixed parameter tractable for graphs of bounded genus
Journal of Algorithms
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Bidimensional Parameters and Local Treewidth
SIAM Journal on Discrete Mathematics
Refined memorization for vertex cover
Information Processing Letters
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
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Graph Theory With Applications
Graph Theory With Applications
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Genus characterizes the complexity of certain graph problems: Some tight results
Journal of Computer and System Sciences
Approximation algorithms via contraction decomposition
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
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Parameterized Algorithms for Generalized Domination
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Algorithms for finding an induced cycle in planar graphs and bounded genus graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Parameterized Complexity for Domination Problems on Degenerate Graphs
Graph-Theoretic Concepts in Computer Science
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
Computational study on planar dominating set problem
Theoretical Computer Science
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Local search: is brute-force avoidable?
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Dynamic programming and planarity: Improved tree-decomposition based algorithms
Discrete Applied Mathematics
How to use planarity efficiently: new tree-decomposition based algorithms
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
An improved algorithm for finding cycles through elements
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs
Journal of Discrete Algorithms
Improved induced matchings in sparse graphs
Discrete Applied Mathematics
Decomposition, approximation, and coloring of odd-minor-free graphs
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
Dynamic programming for graphs on surfaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation algorithms for the capacitated domination problem
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Faster approximation schemes and parameterized algorithms on H-minor-free and odd-minor-free graphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Contraction obstructions for treewidth
Journal of Combinatorial Theory Series B
A simpler algorithm and shorter proof for the graph minor decomposition
Proceedings of the forty-third annual ACM symposium on Theory of computing
Subexponential algorithms for partial cover problems
Information Processing Letters
Journal of Computer and System Sciences
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
Guard games on graphs: Keep the intruder out!
Theoretical Computer Science
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Faster parameterized algorithms for minor containment
Theoretical Computer Science
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximate tree decompositions of planar graphs in linear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast subexponential algorithm for non-local problems on graphs of bounded genus
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Faster approximation schemes and parameterized algorithms on (odd-)H-minor-free graphs
Theoretical Computer Science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Computational study on bidimensionality theory based algorithm for longest path problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Towards fixed-parameter tractable algorithms for abstract argumentation
Artificial Intelligence
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Survey: Subexponential parameterized algorithms
Computer Science Review
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Effective computation of immersion obstructions for unions of graph classes
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Linear time algorithms for finding a dominating set of fixed size in degenerated graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
On the excluded minor structure theorem for graphs of large tree-width
Journal of Combinatorial Theory Series B
FPT algorithms for domination in biclique-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
When is weighted satisfiability FPT?
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
A novel parameterised approximation algorithm for minimum vertex cover
Theoretical Computer Science
A 9k kernel for nonseparating independent set in planar graphs
Theoretical Computer Science
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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We introduce a new framework for designing fixed-parameter algorithms with subexponential running time---2O(&kradic;) nO(1). Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and problems such as vertex cover, feedback vertex set, minimum maximal matching, dominating set, edge dominating set, disk dimension, and many others restricted to bounded-genus graphs (phrased as bipartite-graph problem). 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/or 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 graph-minors work of Robertson and Seymour.Building on these results, we develop subexponential fixed-parameter 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(&kracic;) nh, where h is a constant depending only on H, which is polynomial for k = O(log2 n). 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 and Seymour's graph-minors work. We believe this approach opens the way to further development on problems in H-minor-free graphs.