A separator theorem for graphs of bounded genus
Journal of Algorithms
Efficient parallel solution of linear systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The analysis of a nested dissection algorithm
Numerische Mathematik
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Separators in two and three dimensions
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Automatic domain partitioning in three dimensions
SIAM Journal on Scientific and Statistical Computing
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Separator based parallel divide and conquer in computational geometry
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Multidimensional divide-and-conquer
Communications of the ACM
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
A 3-space partition and its applications
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Disk packings and planar separators
Proceedings of the twelfth annual symposium on Computational geometry
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Moments of inertia and graph separators
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Well-separated pair decomposition for the unit-disk graph metric and its applications
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Studying (non-planar) road networks through an algorithmic lens
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Linear-time algorithms for geometric graphs with sublinearly many crossings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the complexity of approximation streaming algorithms for the k-center problem
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
SIAM Journal on Computing
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
A Deterministic Linear Time Algorithm For Geometric Separators And Its Applications
Fundamenta Informaticae
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We give a deterministic linear time algorithm for finding a smallcost sphere separator of a k-plyneighborhood system &Fgr; in any fixed dimension, where ak-ply neighborhood system inRd is a collection ofn balls such that no points in thespace is covered by more than kballs. The sphere separator intersects at most Ok1dnd-1d balls of &Fgr; and it divides the remaining of &Fgr;into two parts: those in the interior and those in the exterior of thesphere, respectively, so that the larger part contains at most&dgr;n balls d+1d+2d. This result improves the 0(n2) timedeterministic algorithm of Miller and Teng [29] and answers a majoralgorithmic open question posed by Miller, Teng, Thurston and Vavasis[23,25].The deterministic algorithm hinges on the use of a new method forderiving the separator property of neighborhood systems. Using thisalgorithm, we devise an O(kn + n logn) time deterministic algorithm for computing theintersection graph of a k-plyneighborhood system. We give an O(n logn) time algorithm for constructing a linear space,O(log n) query time search structurefor a geometric query problem associated withk-ply neighborhood systems, and weuse this data structure in an algorithm for approximating the value ofk within a constant factor in timeO(n log n). We also develop adeterministic linear time algorithm for finding an Ok1dnd-1d-separator for ak-nearest neighborhood graph ind dimensions.