Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
On linear time minor tests with depth-first search
Journal of Algorithms
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
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Refined Search Tree Technique for DOMINATING SET on Planar Graphs
MFCS '01 Proceedings of the 26th International Symposium on Mathematical 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
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Parameterized complexity: exponential speed-up for planar graph problems
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
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Bidimensionality: new connections between FPT algorithms and PTASs
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)
Journal of Computer and System Sciences
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
The Bidimensional Theory of Bounded-Genus Graphs
SIAM Journal on Discrete Mathematics
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of 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
Computational study on planar dominating set problem
Theoretical Computer Science
Induced Packing of Odd Cycles in a Planar Graph
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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
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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Linear-Time computation of a linear problem kernel for dominating set on planar graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems. The design of such algorithms usually consists of two main steps: first find a branch (or tree) decomposition of the input graph whose width is bounded by a sublinear function of the parameter and, second, use this decomposition to solve the problem in time that is single exponential to this bound. The main tool for the first step is the Bidimensionality Theory. Here we present not only the potential, but also the boundaries, of this theory. For the second step, we describe recent techniques, associating the analysis of subexponential algorithms to combinatorial bounds related to Catalan numbers. As a result, we have 2^O^(^k^)@?n^O^(^1^) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.