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
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A deterministic linear time algorithm for geometric separators and its applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Geometric Separators for Finite-Element Meshes
SIAM Journal on Scientific Computing
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Separator-based strategies for efficient message routing
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
ICS '96 Proceedings of the 10th international conference on Supercomputing
Testing bipartiteness of geometric intersection graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
Improved sublinear time algorithm for width-bounded separators
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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We give a deterministic linear time algorithm for finding a “good” sphere separator of a k-ply neighborhood system Φ in any fixed dimension, where a k-ply neighborhood system in $$\IR$$d is a collection of n balls such that no points in the space is covered by more than k balls. The separating sphere intersects at most O (k1/dn1−1/d) balls of Φ and divides the remaining of Φ into two parts: those in the interior and those in the exterior of the sphere, respectively, so that the larger part contains at most δn balls ((d + 1)/(d + 2) 2) time deterministic algorithm of Miller and Teng [30] and answers a major algorithmic open question posed by Miller, Teng, Thurston, and Vavasis [23, 26]. The deterministic algorithm hinges on the use of a new method for deriving the separator property of neighborhood systems. Using this algorithm, we devise an O(kn+nlogn) time deterministic algorithm for computing the intersection graph of a k-ply neighborhood system. We give an O(nlogn) time algorithm for constructing a linear space, O(logn) query time search structure for a geometric query problem associated with k-ply neighborhood systems, and we use this data structure in an algorithm for approximating the value of k within a constant factor in time O(nlogn). We also develop a deterministic linear time algorithm for finding an O (k1/dn1−1/d)-separator for a k-nearest neighborhood graph in d dimensions.