Covering all cliques of a graph
Discrete Mathematics - Topics on domination
The colour theorems of Brooks and Gallai extended
Discrete Mathematics
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Test-Suite Reduction and Prioritization for Modified Condition/Decision Coverage
IEEE Transactions on Software Engineering
A Parallel Approximation Hitting Set Algorithm for Gene Expression Analysis
SBAC-PAD '02 Proceedings of the 14th Symposium on Computer Architecture and High Performance Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
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
Almost 2-SAT is fixed-parameter tractable
Journal of Computer and System Sciences
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
Betweenness parameterized above tight lower bound
Journal of Computer and System Sciences
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Vertex Cover Problem Parameterized Above and Below Tight Bounds
Theory of Computing Systems
Interference in cellular networks: the minimum membership set cover problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Nonblocker: parameterized algorithmics for minimum dominating set
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
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
Parameterized study of the test cover problem
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Hi-index | 5.23 |
In the Hitting Set problem, we are given a collection F of subsets of a ground set V and an integer p, and asked whether V has a p-element subset that intersects each set in F. We consider two parameterizations of Hitting Set below tight upper bounds, p=m-k and p=n-k. In both cases k is the parameter. We prove that the first parameterization is fixed-parameter tractable, but has no polynomial kernel unless coNP @? NP/poly. The second parameterization is W[1]-complete, but the introduction of an additional parameter, the degeneracy of the hypergraph H=(V,F), makes the problem not only fixed-parameter tractable, but also one with a linear kernel. Here the degeneracy of H=(V,F) is the minimum integer d such that for each X@?V the hypergraph with vertex set V@?X and edge set containing all edges of F without vertices in X, has a vertex of degree at most d. In Nonblocker (Directed Nonblocker), we are given an undirected graph (a directed graph) G on n vertices and an integer k, and asked whether G has a set X of n-k vertices such that for each vertex y@?X there is an edge (arc) from a vertex in X to y. Nonblocker can be viewed as a special case of Directed Nonblocker (replace an undirected graph by a symmetric digraph). Dehne et al. (Proc. SOFSEM 2006) proved that Nonblocker has a linear-order kernel. We obtain a linear-order kernel for Directed Nonblocker.