Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Journal of Combinatorial Theory Series B
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
The Parameterized Complexity of Counting Problems
SIAM Journal on Computing
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
Parameterized algorithms for feedback set problems and their duals in tournaments
Theoretical Computer Science - Parameterized and exact computation
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Theory of Computing Systems
On the Optimality of Planar and Geometric Approximation Schemes
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
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Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A fixed-parameter algorithm for the directed feedback vertex set problem
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Improved algorithms for feedback vertex set problems
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Finding paths of length k in O∗(2k) time
Information Processing Letters
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Randomized algorithms for the loop cutset problem
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On problems without polynomial kernels
Journal of Computer and System Sciences
Almost 2-SAT is fixed-parameter tractable
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Closest Substring Problems with Small Distances
SIAM Journal on Computing
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
The Complexity of Satisfiability of Small Depth Circuits
Parameterized and Exact Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Planarity Allowing Few Error Vertices in Linear Time
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
An improved kernelization algorithm for r-Set Packing
Information Processing Letters
Improved upper bounds for vertex cover
Theoretical Computer Science
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the possibility of faster SAT algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Exact Exponential Algorithms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Digraph decompositions and monotonicity in digraph searching
Theoretical Computer Science
Satisfiability certificates verifiable in subexponential time
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Tournament immersion and cutwidth
Journal of Combinatorial Theory Series B
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Kernelization of packing problems
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
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fixed-parameter tractability of directed multiway cut parameterized by the size of the cutset
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
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Faster Parameterized Algorithms for Minimum Fill-in
Algorithmica
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Algorithmica
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WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On multiway cut parameterized above lower bounds
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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Discrete Optimization
Discrete Optimization
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Operations Research Letters
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The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
An improved parameterized algorithm for the minimum node multiway cut problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parameterized Complexity
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
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The progress in parameterized complexity has been very significant in recent years, with new research questions and directions, such as kernelization lower bounds, appearing and receiving considerable attention. This speculative article tries to identify new directions that might become similar hot topics in the future. First, we point out that the search for optimality in parameterized complexity already has good foundations, but lots of interesting work can be still done in this area. The systematic study of kernelization became a very successful research direction in recent years. We look at what general conclusions one can draw from these results and we argue that the systematic study of other algorithmic techniques should be modeled after the study of kernelization. In particular, we set up a framework for understanding which problems can be solved by branching algorithms. Finally, we discuss that the domain of directed graph problems is a challenging area which can potentially see significant progress in the following years.