Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Invitation to data reduction and problem kernelization
ACM SIGACT News
A Linear Kernel for the k-Disjoint Cycle Problem on Planar Graphs
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
On problems without polynomial kernels
Journal of Computer and System Sciences
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Two Edge Modification Problems without Polynomial Kernels
Parameterized and Exact Computation
Approximation Algorithms for Treewidth
Algorithmica
A Cubic Kernel for Feedback Vertex Set and Loop Cutset
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Lower Bounds for Kernelizations and Other Preprocessing Procedures
Theory of Computing Systems
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
Clique cover and graph separation: new incompressibility results
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Induced disjoint paths in claw-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Restricted and swap common superstring: a parameterized view
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Parameterized algorithmics and computational experiments for finding 2-clubs
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
On the Parameterized Complexity and Kernelization of the Workflow Satisfiability Problem
ACM Transactions on Information and System Security (TISSEC)
Incremental list coloring of graphs, parameterized by conservation
Theoretical Computer Science
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
Kernel bounds for path and cycle problems
Theoretical Computer Science
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
Note: Parameterized complexity of k-Chinese Postman Problem
Theoretical Computer Science
On the Hardness of Losing Width
Theory of Computing Systems
Hi-index | 5.23 |
In this paper, we show that the problems Disjoint Cycles and Disjoint Paths do not have polynomial kernels, unless NP@?coNP/poly. Thus, these problems do not allow polynomial time preprocessing that results in instances whose size is bounded by a polynomial in the parameter at hand. We build upon recent results by Bodlaender et al. [6] and Fortnow and Santhanam [20], that show that NP-complete problems that are 'or-compositional' do not have polynomial kernels, unless NP@?coNP/poly. To this machinery, we add a notion of transformation, and obtain that Disjoint Cycles, and Disjoint Paths do not have polynomial kernels, unless NP@?coNP/poly. For the proof, we introduce a problem on strings, called Disjoint Factors, and first show that this problem has no polynomial kernel unless NP@?coNP/poly. We also show that the related Disjoint Cycles Packing problem has a kernel of size O(klogk).