A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
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
Kernelization for cycle transversal problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
On the small cycle transversal of planar graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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
An improved kernel for planar connected dominating set
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
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
Feedback vertex set in mixed graphs
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Linear problem kernels for planar graph problems with small distance property
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Parameterized complexity of vertex deletion into perfect graph classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Hitting and harvesting pumpkins
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
Weak compositions and their applications to polynomial lower bounds for kernelization
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
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
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
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On the hardness of losing width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Simpler linear-time kernelization for planar dominating set
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
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Discrete 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
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
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
What's next? future directions in parameterized complexity
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
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
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
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
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
Improved linear problem kernel for planar connected dominating set
Theoretical Computer Science
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
On the Hardness of Losing Width
Theory of Computing Systems
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Polynomial time preprocessing to reduce instance size is one of the most commonly deployed heuristics to tackle computationally hard problems. In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, we can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this paper, we show that all problems expressible in Counting Monadic Second Order Logic and satisfying a compactness property admit a polynomial kernel on graphs of bounded genus. Our second result is that all problems that have finite integer index and satisfy a weaker compactness condition admit a linear kernel on graphs of bounded genus. The study of kernels on planar graphs was initiated by a seminal paper of Alber, Fellows, and Niedermeier [J. ACM, 2004 ] who showed that Planar Dominating Set admits a linear kernel. Following this result, a multitude of problems have been shown to admit linear kernels on planar graphs by combining the ideas of Alber et al. with problem specific reduction rules. Our theorems unify and extend all previously known kernelization results for planar graph problems. Combining our theorems with the Erdos-Posa property we obtain various new results on linear kernels for a number of packing and covering problems.