Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On the Compressibility of NP Instances and Cryptographic Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
The parameterized complexity of the unique coverage problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Kernelization algorithms for d-hitting set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On making a distinguished vertex minimum degree by vertex deletion
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Facility location problems: A parameterized view
Discrete Applied Mathematics
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
Theoretical Computer Science
Pattern-guided data anonymization and clustering
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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
Kernelization of packing problems
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
Parameterized Eulerian strong component arc deletion problem on tournaments
Information Processing Letters
Polynomial kernels for hard problems on disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
FPT algorithms for connected feedback vertex set
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
From few components to an eulerian graph by adding arcs
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
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
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Discrete Optimization
FPT algorithms for Connected Feedback Vertex Set
Journal of Combinatorial Optimization
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
Fixed-parameter tractability of satisfying beyond the number of variables
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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
Deterministic parameterized connected vertex cover
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs
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)
FPT algorithms for domination in biclique-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
European Journal of Combinatorics
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
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
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
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
Kernel bounds for path and cycle problems
Theoretical Computer Science
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
On the Hardness of Losing Width
Theory of Computing Systems
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In parameterized complexity each problem instance comes with a parameter k , and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k . Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existence of polynomial kernels has been developed by Bodlaender et al. [4] and Fortnow and Santhanam [9]. In this paper we show how to combine these results with combinatorial reductions which use colors and IDs in order to prove kernelization lower bounds for a variety of basic problems: We show that the Steiner Tree problem parameterized by the number of terminals and solution size k , and the Connected Vertex Cover and Capacitated Vertex Cover problems do not admit a polynomial kernel. The two latter results are surprising because the closely related Vertex Cover problem admits a kernel of size 2k . Alon and Gutner obtain a k poly (h ) kernel for Dominating Set in H -Minor Free Graphs parameterized by h = |H | and solution size k and ask whether kernels of smaller size exist [2]. We partially resolve this question by showing that Dominating Set in H -Minor Free Graphs does not admit a kernel with size polynomial in k + h . Harnik and Naor obtain a "compression algorithm" for the Sparse Subset Sum problem [13]. We show that their algorithm is essentially optimal since the instances cannot be compressed further. Hitting Set and Set Cover admit a kernel of size k O (d ) when parameterized by solution size k and maximum set size d . We show that neither of them, along with the Unique Coverage and Bounded Rank Disjoint Sets problems, admits a polynomial kernel. All results are under the assumption that the polynomial hierarchy does not collapse to the third level. The existence of polynomial kernels for several of the problems mentioned above were open problems explicitly stated in the literature [2,3,11,12,14]. Many of our results also rule out the existence of compression algorithms, a notion similar to kernelization defined by Harnik and Naor [13], for the problems in question.