Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Graphs with small bandwidth and cutwidth
Discrete Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Easy problems for tree-decomposable graphs
Journal of Algorithms
On well-partial-order theory and its application to combinatorial problems of VLSI design
SIAM Journal on Discrete Mathematics
SIAM Journal on Computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Graph classes: a survey
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Reduction algorithms for graphs of small treewidth
Information and Computation
On weighted vs unweighted versions of combinatorial optimizationproblems
Information and Computation
Vertex cover: further observations and further improvements
Journal of Algorithms
Algorithms column: the vertex cover problem
ACM SIGACT News
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
The Parameterized Complexity of Some Problems in Logic and Linguistics
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Fast Self-Reduction Algorithms for Combinatorical Problems of VLSI-Design
AWOC '88 Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures
Parameterized complexity of vertex colouring
Discrete Applied Mathematics
On efficient fixed-parameter algorithms for weighted vertex cover
Journal of Algorithms
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)
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
Invitation to data reduction and problem kernelization
ACM SIGACT News
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
König Deletion Sets and Vertex Covers above the Matching Size
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
On problems without polynomial kernels
Journal of Computer and System Sciences
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
Going weighted: Parameterized algorithms for cluster editing
Theoretical Computer Science
A multivariate complexity analysis of determining possible winners given incomplete votes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Well-Quasi-Orders in Subclasses of Bounded Treewidth Graphs
Parameterized and Exact Computation
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The complexity of finding subgraphs whose matching number equals the vertex cover number
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Improving exhaustive search implies superpolynomial lower bounds
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
Improved upper bounds for vertex cover
Theoretical Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Monadic second order logic on graphs with local cardinality constraints
ACM Transactions on Computational Logic (TOCL)
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Vertex Cover Problem Parameterized Above and Below Tight Bounds
Theory of Computing Systems
Deconstructing intractability-A multivariate complexity analysis of interval constrained coloring
Journal of Discrete Algorithms
Parameterized complexity of coloring problems: Treewidth versus vertex cover
Theoretical Computer Science
Improved deterministic algorithms for weighted matching and packing problems
Theoretical Computer Science
Finding topological subgraphs is fixed-parameter tractable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Matching and P2-packing: weighted versions
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Problems parameterized by treewidth tractable in single exponential time: a logical approach
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Parameterized complexity of vertex deletion into perfect graph classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Paths, flowers and vertex cover
ESA'11 Proceedings of the 19th European conference on Algorithms
A kernel of order 2k-clogk for vertex cover
Information Processing Letters
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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Two-Layer planarization parameterized by feedback edge set
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Kernelization for maximum leaf spanning tree with positive vertex weights
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
On multiway cut parameterized above lower bounds
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
Kernel bounds for path and cycle problems
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
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Algorithmic Meta-theorems for Restrictions of Treewidth
Algorithmica - Special Issue: Parameterized and Exact Computation, Part I
Representative Sets and Irrelevant Vertices: New Tools for Kernelization
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
On explaining integer vectors by few homogenous segments
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
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The aim of this article is to motivate and describe the parameter ecology program, which studies how different parameters contribute to the difficulty of classical problems. We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or polynomial kernels. An extensive overview of recent advances on this front is presented for the Vertex Cover problem. Moving even beyond the parameter ecology program we advocate the principle of model enrichment, which raises the challenge of generalizing positive results to problem definitions with greater modeling power. The computational intractability which inevitably emerges can be deconstructed by introducing additional parameters, leading towards a theory of fully multivariate algorithmics.