A separator theorem for graphs of bounded genus
Journal of Algorithms
An application of the Planar Separator Theorem to counting problems
Information Processing Letters
A study on two geometric location problems
Information Processing Letters
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Separators in two and three dimensions
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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
SIAM Journal on Discrete Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Disk packings and planar separators
Proceedings of the twelfth annual symposium on Computational geometry
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Introduction to VLSI Systems
Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Graph Separators: A Parameterized View
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Geometric Separator Theorems and Applications
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric Separators and Their Applications to Protein Folding in the HP-Model
SIAM Journal on Computing
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
C 900--An Advanced Mobile Radio Telephone System with Optimum Frequency Utilization
IEEE Journal on Selected Areas in Communications
Strong I/O lower bounds for binomial and FFT computation graphs
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any fixed d-dimensional Euclidean space. The separator is applied in obtaining 2^O^(^n^) time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take n^O^(^n^) time. One of those problems is the well-known disk covering problem, which seeks to determine the minimal number of fixed size disks to cover n points on a plane. They also include some NP-hard problems on disk graphs such as the maximum independent set problem, the vertex cover problem, and the minimum dominating set problem. For a constant a0 and a set of points Q on the plane, an a-wide separator is the region between two parallel lines of distance a that partitions Q into Q"1 (on the left side of the region), S (inside the region), and Q"2 (on the right side of the region). If the distance is at least one between every two points in the set Q with n points, there is an a-wide separator that partitions Q into Q"1, S and Q"2 such that |Q"1|,|Q"2|=