On the Solution of Linear Recurrence Equations
Computational Optimization and Applications
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Reduction algorithms for graphs of small treewidth
Information and Computation
Vertex cover: further observations and further improvements
Journal of Algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Bidimensional Parameters and Local Treewidth
SIAM Journal on Discrete Mathematics
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Linear Kernel for the k-Disjoint Cycle Problem on Planar Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Linear Kernel for Planar Connected Dominating Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The parameterized complexity of the induced matching problem in planar graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Parametric duality and kernelization: lower bounds and upper bounds on kernel size
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Fixed-parameter tractability results for full-degree spanning tree and its dual
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Survey: Subexponential parameterized algorithms
Computer Science Review
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A linear kernel for a planar connected dominating set
Theoretical Computer Science
On the small cycle transversal of planar graphs
Theoretical Computer Science
Contraction obstructions for treewidth
Journal of Combinatorial Theory Series B
Journal of Computer and System Sciences
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
On parameterized independent feedback vertex set
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Co-nondeterminism in compositions: a kernelization lower bound for a Ramsey-type problem
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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Polynomial kernels for hard problems on disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
FPT algorithms for connected feedback vertex set
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
On the hardness of losing width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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
Discrete Optimization
FPT algorithms for Connected Feedback Vertex Set
Journal of Combinatorial Optimization
Kernels for packing and covering problems
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Kernel(s) for problems with no kernel: On out-trees with many leaves
ACM Transactions on Algorithms (TALG)
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
A single-exponential FPT algorithm for the K4- minor cover problem
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)
European Journal of Combinatorics
Nonblocker in h-minor free graphs: kernelization meets discharging
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
An improved kernel for the undirected planar feedback vertex set problem
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
A 9k kernel for nonseparating independent set in planar graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On the parameterized complexity of finding separators with non-hereditary properties
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Planar graph vertex partition for linear problem kernels
Journal of Computer and System Sciences
Note: Towards optimal kernel for connected vertex cover in planar graphs
Discrete Applied Mathematics
Linear kernels and single-exponential algorithms via protrusion decompositions
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
When is weighted satisfiability FPT?
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
A 9k kernel for nonseparating independent set in planar graphs
Theoretical Computer Science
On the Hardness of Losing Width
Theory of Computing Systems
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Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on H-minor free graphs. Demaine and Hajiaghayi [SODA 2005] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this paper, we establish a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In parameterized complexity, each problem instance comes with a parameter k and the parameterized problem is said to admit a linear kernel if there is a polynomial time algorithm, called a kernelization algorithm, that reduces the input instance to an equivalent instance (called kernel) with size linearly bounded by k. We show that "essentially" all bidimensional problems not only have sub-exponential time algorithms and PTASs but they also have linear kernels, affirmatively answering an open question from [J. ACM 2005] where the existence of linear kernels was conjectured for the first time. In particular, we prove that every minor (respectively contraction) bidimensional problem that satisfies the separation property and is of finite integer index, admits a linear kernel for classes of graphs that exclude a fixed graph (respectively an apex graph H) H as a minor. Recently, Bodlaender et al. [FOCS 2009] laid the foundation for obtaining meta-algorithmic results for kernelization and showed that various problems satisfying some logical and compactness properties have polynomial, even linear kernels on graphs of bounded genus. With the use of bidimensionality we are able to extend these results to minor-free and apex-minor-free graphs. Our results imply that a multitude of bidimensional problems, which include Dominating Set, Feedback Vertex Set, Edge Dominating Set, Vertex Cover, r-Dominating Set, Connected Dominating Set, Cycle Packing, Connected Vertex Cover, Almost Constant Treewidth, and various other vertex covering and packing problems, admit linear kernels on the corresponding graph classes. For most of these problems no polynomial kernels on H-minor-free graphs were known prior to our work.