Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
Optimization-Based Peptide Mass Fingerprinting for Protein Mixture Identification
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Shared Peptides in Mass Spectrometry Based Protein Quantification
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
Some fixed-parameter tractable classes of hypergraph duality and related problems
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Enumerate and expand: new runtime bounds for vertex cover variants
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Parameterized algorithms for HITTING SET: the weighted case
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
EDGE DOMINATING SET: efficient enumeration-based exact algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity
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Motivated by the need for succinct representations of all ''small'' transversals (or hitting sets) of a hypergraph of fixed rank, we study the complexity of computing such a representation. Next, the existence of a minimal hitting set of at least a given size arises as a subproblem. We give one algorithm for hypergraphs of any fixed rank, and we largely improve an earlier algorithm (by H. Fernau, 2005, [10]) for the rank-2 case, i.e., for computing a minimal vertex cover of at least a given size in a graph. We were led to these questions by combinatorial aspects of the protein inference problem in shotgun proteomics.