Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Extremal polygon containment problems
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Journal of Algorithms
Randomized optimal algorithm for slope selection
Information Processing Letters
A deterministic poly(log log N)-time N-processor algorithm for linear programming in fixed dimension
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computing a segment center for a planar point set
Journal of Algorithms
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
An efficient algorithm for the Euclidean two-center problem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
ACM Computing Surveys (CSUR)
Efficient randomized algorithms for some geometric optimization problems
Proceedings of the eleventh annual symposium on Computational geometry
A near-linear algorithm for the planar 2-center problem
Proceedings of the twelfth annual symposium on Computational geometry
Approximating monotone polygonal curves using the uniform metric
Proceedings of the twelfth annual symposium on Computational geometry
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On enumerating and selecting distances
Proceedings of the fourteenth annual symposium on Computational geometry
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A fast algorithm for the alpha-connected two-center decision problem
Information Processing Letters
New algorithms for barrier coverage with mobile sensors
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
On some geometric selection and optimization problems via sorted matrices
Computational Geometry: Theory and Applications
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We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo. Our new approach is based on expander graphs and is conceptually much simpler and has more explicit geometric flavor. It does not require parallelization or randomization, and it exploits recent range-searching techniques of Matousˇek and others. We exemplify the technique on three problems, the slope selection problem, the planar distance selection problem, and the planar two-center problem. For the first problem we develop an O(n log3n)) solution, which, although suboptimal, is very simple. The second and third problems are more typical examples of our approach. Our solutions have, respectively, running time O(n4/3 log3+&dgr; n), for any &dgr; 0, and O(n2 log3 n), comparable with the respective solutions of [2, 5].