Guest Editors' Foreword

Bettina Speckmann, Csaba D. Tóth
2020 Discrete & Computational Geometry  
A record number of 206 papers were submitted to SoCG 2018, of which the Program Committee accepted 73 for presentation. This special issue of Discrete & Computational Geometry contains the full versions of seven especially strong papers from the symposium, recommended by the Program Committee. These papers were submitted, reviewed, and revised according to the usual high standards of D&CG. We thank the authors of all submitted papers for revising and polishing their work. We are grateful to the
more » ... anonymous referees for their dedication and expertise, which ensured the high quality of the papers in this special issue. The papers appear here in alphabetical order of the names of the first authors. In the remainder of this foreword we briefly introduce all papers, arranging them into broad topics. Geometric Hitting Sets and Set Covers Capacitated covering problems in geometric range spaces are variants of the set cover problem, with constraints on the maximum number of points assigned to each range in the cover. Sayan Bandyapadhyay, Santanu Bhowmick, Tanmay Inamdar, and Kasturi Varadarajan consider covering a set of points in R d by the minimum number of balls, subject to capacity constraints for each ball. The problem is known to be hard to approximate in Euclidean spaces. The authors present bicriteria approximation results, approximating the cost while expanding the balls by a constant factor (but not changing the capacities), using a novel rounding scheme for the natural LP-relaxation of these problems that can handle balls of widely different radii. The Hadwiger-Debrunner number HD d ( p, q), q ≥ d + 1, is the minimum number of points that can pierce any family of convex bodies in R d with the ( p, q)-property
doi:10.1007/s00454-020-00212-0 fatcat:c7rkm2wq4vax7kdvpn7urjbl7e