A Quadratic Kernel for 3-Set Packing
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Algorithms and Experiments for Clique Relaxations--Finding Maximum s-Plexes
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
A Linear Vertex Kernel for Maximum Internal Spanning Tree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
An improved kernelization algorithm for r-Set Packing
Information Processing Letters
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
A linear kernel for co-path/cycle packing
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
On bounded block decomposition problems for under-specified systems of equations
Journal of Computer and System Sciences
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Exact combinatorial algorithms and experiments for finding maximum k-plexes
Journal of Combinatorial Optimization
Kernelization algorithms for d-hitting set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
A linear vertex kernel for maximum internal spanning tree
Journal of Computer and System Sciences
European Journal of Combinatorics
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Crown structures in a graph are defined and shown to be useful in kernelization algorithms for the classic vertex cover problem. Two vertex cover kernelization methods are discussed. One, based on linear programming, has been in prior use and is known to produce predictable results, although it was not previously associated with crowns. The second, based on crown structures, is newer and much faster, but produces somewhat variable results. These two methods are studied and compared both theoretically and experimentally with each other and with older, more primitive kernelization algorithms. Properties of crowns and methods for identifying them are discussed. Logical connections between linear programming and crown reductions are established. It is shown that the problem of finding an induced crown-free subgraph, and the problem of finding a crown of maximum size in an arbitrary graph, are solvable in polynomial time.