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Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

://orcid.org/0000-0001-6553-7317 4 Timothy M. Chan University of Illinois at Urbana-Champaign , U.S.A 5 Alexander Wolff Universität Würzburg , Germany https://orcid.org/0000-0001-5872-718X 6 Joachim Spoerhase ... Optimal Set Covers in Finite VCDimension . Discrete Comput. Geom. , 14 ( 4 ): 463 - 479 , 1995 . doi: 10 .1007/BF02570718. Timothy M. Chan and Elyot Grant . Exact Algorithms and APX-hardness Results for

Approximation Algorithms for Maximum Independent Set of Pseudo-Disks

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local-search algorithm yields a PTAS. For the weighted case, we suggest a novel rounding scheme based on an LP relaxation of the problem, which leads to a constant-factor approximation.Most previous...

Dynamic Coresets

Discrete Comput Geom Timothy M. Chan 0 0 T.M. Chan ( ) School of Computer Science, University of Waterloo , Waterloo, Ontario N2L 3G1 , Canada We give a dynamic data structure that can maintain an