Guest Editors' Foreword

Siu-Wing Cheng, Olivier Devillers
<span title="2015-03-05">2015</span> <i title="Springer Nature America, Inc"> <a target="_blank" rel="noopener" href="" style="color: black;">Discrete &amp; Computational Geometry</a> </i> &nbsp;
This special issue of Discrete & Computational Geometry contains a selection of seven papers whose preliminary versions appeared in the Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, June 8-11, 2014. The seven papers in this issue were invited, submitted, and then reviewed according to the usual, high standards of the journal. These papers cover a wide spectrum of topics in computational geometry. Chan and Lee propose algorithms for a number of geometric problems
more &raquo; ... the comparison-based model that achieve optimality in the constant factors of the leading terms. The problems include 2D and 3D maxima, 2D convex hull, segment intersection searching, and point location among axis-parallel boxes in 3D or in a 3D box subdivision. Bonichon, Kanj, Perković, and Xia study the maximum degree of a plane spanner with constant stretch. There is a known lower bound of three, and there has been a series of results that gradually reduce the maximum degree to six. This paper presents a new upper bound of four which almost closes the gap between the upper and lower bounds. Har-Peled and Raichel give a near linear bound on the expected complexity of the multiplicatively weighted Voronoi diagram of n sites in the plane. The locations of the sites are fixed, and the sites can be points, segments, or convex sets. The weights of the sites may be a random sample from a distribution or a random permutation of n
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/s00454-015-9680-3</a> <a target="_blank" rel="external noopener" href="">fatcat:3j56wwx2j5fe7emkodkxjc4wcm</a> </span>
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