The Clarkson–Shor Technique Revisited and Extended

MICHA SHARIR

doi:10.1017/S0963548302005527

Abstract

We provide an alternative, simpler and more general derivation of the Clarkson–Shor probabilistic technique [7] and use it to obtain several extensions and new combinatorial bounds.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Alon, Noga Pach, János Pinchasi, Rom Radoičić, Radoš and Sharir, Micha 2005. Crossing patterns of semi-algebraic sets. Journal of Combinatorial Theory, Series A, Vol. 111, Issue. 2, p. 310.

Aronov, Boris and Har-Peled, Sariel 2008. On Approximating the Depth and Related Problems. SIAM Journal on Computing, Vol. 38, Issue. 3, p. 899.

Setter, Ophir Sharir, Micha and Halperin, Dan 2009. Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space. p. 43.

Cabello, S. Fort, M. and Sellarès, J.A. 2009. Higher-order Voronoi diagrams on triangulated surfaces. Information Processing Letters, Vol. 109, Issue. 9, p. 440.

Rafalin, Eynat Souvaine, Diane L. and Tóth, Csaba D. 2010. Cuttings for Disks and Axis-Aligned Rectangles in Three-Space. Discrete & Computational Geometry, Vol. 43, Issue. 2, p. 221.

Setter, Ophir Sharir, Micha and Halperin, Dan 2010. Transactions on Computational Science IX. Vol. 6290, Issue. , p. 1.

Har-Peled, Sariel 2014. Quasi-Polynomial Time Approximation Scheme for Sparse Subsets of Polygons. p. 120.

Ackerman, Eyal Fox, Jacob Pach, János and Suk, Andrew 2014. On grids in topological graphs. Computational Geometry, Vol. 47, Issue. 7, p. 710.

Cheilaris, Panagiotis Khramtcova, Elena Langerman, Stefan and Papadopoulou, Evanthia 2016. A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters. Algorithmica, Vol. 76, Issue. 4, p. 935.

Papadopoulou, Evanthia and Zavershynskyi, Maksym 2016. The Higher-Order Voronoi Diagram of Line Segments. Algorithmica, Vol. 74, Issue. 1, p. 415.

Chang, Hsien-Chih Har-Peled, Sariel and Raichel, Benjamin 2016. From Proximity to Utility: A Voronoi Partition of Pareto Optima. Discrete & Computational Geometry, Vol. 56, Issue. 3, p. 631.

Liu, Chih-Hung and Montanari, Sandro 2018. Minimizing the Diameter of a Spanning Tree for Imprecise Points. Algorithmica, Vol. 80, Issue. 2, p. 801.

Pach, János and Tóth, Géza 2018. Graph Drawing and Network Visualization. Vol. 10692, Issue. , p. 153.

Adamaszek, Anna Har-Peled, Sariel and Wiese, Andreas 2019. Approximation Schemes for Independent Set and Sparse Subsets of Polygons. Journal of the ACM, Vol. 66, Issue. 4, p. 1.

Pach, János and Tóth, Géza 2019. Many touchings force many crossings. Journal of Combinatorial Theory, Series B, Vol. 137, Issue. , p. 104.

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The Clarkson–Shor Technique Revisited and Extended

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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The Clarkson–Shor Technique Revisited and Extended

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