Discrete Mathematics - Topics on domination
Computing the smallest k-enclosing circle and related problems
Computational Geometry: Theory and Applications
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Invitation to data reduction and problem kernelization
ACM SIGACT News
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
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
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Efficient approximation schemes for geometric problems?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Parameterized complexity of independence and domination on geometric graphs
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Kernelization is a powerful tool to obtain fixed-parameter tractable algorithms. Recent breakthroughs show that many graph problems admit small polynomial kernels when restricted to sparse graph classes such as planar graphs, bounded-genus graphs or H-minor-free graphs. We consider the intersection graphs of (unit) disks in the plane, which can be arbitrarily dense but do exhibit some geometric structure. We give the first kernelization results on these dense graph classes. Connected Vertex Cover has a kernel with 12k vertices on unit-disk graphs and with 3k2+7k vertices on disk graphs with arbitrary radii. Red-Blue Dominating Set parameterized by the size of the smallest color class has a linear-vertex kernel on planar graphs, a quadratic-vertex kernel on unit-disk graphs and a quartic-vertex kernel on disk graphs. Finally we prove that H-Matching on unit-disk graphs has a linear-vertex kernel for every fixed graph H.