Discrete Mathematics - Topics on domination
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A deterministic linear time algorithm for geometric separators and its applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Exact Algorithms and Approximation Schemes for Base Station Placement Problems
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Which Problems Have Strongly Exponential Complexity?
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Parameterized Complexity
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Theory and application of width bounded geometric separators
Journal of Computer and System Sciences
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Theory and application of width bounded geometric separator
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Efficient approximation schemes for geometric problems?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Polynomial kernels for hard problems on disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Compact and low delay routing labeling scheme for Unit Disk Graphs
Computational Geometry: Theory and Applications
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
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We consider the parameterized probleln, whether for a given set D of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time nO(√k) that is--to our knowledge--the first algorithm with running time bounded by an exponential with a sublinear exponent. For γ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time 2O(√k) + nO(1). The results are based on problem kernelization and a new "geometric (√ċ--separator) theorem" which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a "geometric problem kernelization" and, in a second step, uses divide-and-conquer based on our new "geometric separator theorem."