http://jocg.org/index.php/jocg/issue/feedJournal of Computational Geometry2017-04-25T10:05:40-04:00Managing Editorsjocg@jocg.orgOpen Journal SystemsThe Journal of Computational Geometry (JoCG) is an international open access journal devoted to publishing original research of the highest quality in all aspects of computational geometry.<p>JoCG articles and supplementary data are freely available for download and JoCG charges no publishing fees of any kind.</p><p>All JoCG issues and articles are assigned a DOI. JoCG's data and content are safeguarded through <a href="/index.php/jocg/pages/view/backup">several backup mechanisms</a>.</p>http://jocg.org/index.php/jocg/article/view/289Approximating minimum-area rectangular and convex containers for packing convex polygons2017-04-25T09:51:29-04:00Helmut Altalt@mi.fu-berlin.deMark de Bergmdberg@win.tue.nlChristian Knauerchristian.knauer@uni-bayreuth.deWe investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms.2017-02-18T14:30:53-05:00Copyright (c) 2017 Journal of Computational Geometryhttp://jocg.org/index.php/jocg/article/view/295Towards plane spanners of degree 32017-04-25T09:51:29-04:00Ahmad Biniazahmad.biniaz@gmail.comProsenjit Bosejit@scs.carleton.caJean-Lou De Carufeljdecaruf@uottawa.caCyril Gavoillegavoille@labri.frAnil Maheshwarianil@scs.carleton.caMichiel Smidmichiel@scs.carleton.ca<p>Let $S$ be a finite set of points in the plane. In this paper we consider the problem of computing plane spanners of degree at most three for $S$.</p><ol><li>If $S$ is in convex position, then we present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner for $S$ whose vertex degree is at most 3. </li><li>If $S$ is the vertex set of a non-uniform rectangular lattice, then we present an algorithm that constructs a plane $3\sqrt{2}$-spanner for $S$ whose vertex degree is at most 3. </li><li>If $S$ is in general position, then we show how to compute plane degree-3 spanners for $S$ with a linear number of Steiner points.</li></ol>2017-03-13T11:48:39-04:00Copyright (c) 2017 Journal of Computational Geometryhttp://jocg.org/index.php/jocg/article/view/297On interference among moving sensors and related problems2017-04-25T09:51:29-04:00Jean-Lou De Carufeljdecaruf@uottawa.caMatthew J. Katzmatya@cs.bgu.ac.ilMatias Kormanmati@dais.is.tohoku.ac.jpAndré van Renssenandre@nii.ac.jpMarcel Roeloffzenmarcel@nii.ac.jpShakhar Smorodinskyshakhar@math.bgu.ac.il<p>We show that for any set of $n$ moving points in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the points of size $O(k \log k)$, such that the Voronoi diagram of this subset is ``balanced'' at any given time (i.e., it contains $O(n/k)$ points per cell). We also show that the bound $O(k \log k)$ is near optimal even for the one dimensional case in which points move linearly in time. As an application, we show that one can assign communication radii to the sensors of a network of $n$ moving sensors so that at any given time, their interference is $O(\sqrt{n\log n})$. This is optimal up to an $O(\sqrt{\log n})$ factor. In order to obtain these results, we extend well-known results from $\varepsilon$-net theory to kinetic environments.</p>2017-04-25T09:08:54-04:00Copyright (c) 2017 Journal of Computational Geometryhttp://jocg.org/index.php/jocg/article/view/280Counting and enumerating crossing-free geometric graphs2017-04-25T10:05:40-04:00Manuel Wettsteinmw@inf.ethz.ch<p>We describe a framework for constructing data structures which allow fast counting and enumeration of various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, who used them to count triangulations in time $O(2^nn^2)$ where $n$ is the number of points. The main idea is to represent geometric graphs as source-sink paths in a directed acyclic graph.</p><p>The following results will emerge. The number of all crossing-free geometric graphs can be computed in time $O(c^nn^4)$ for some $c < 2.83929$. The number of crossing-free convex partitions can be computed in time $O(2^nn^4)$. The number of crossing-free perfect matchings can be computed in time $O(2^nn^4)$. The number of convex subdivisions can be computed in time $O(2^nn^4)$. The number of crossing-free spanning trees can be computed in time $O(c^nn^4)$ for some $c < 7.04313$. The number of crossing-free spanning cycles can be computed in time $O(c^nn^4)$ for some $c < 5.61804$.</p><p>Moreover, after a preprocessing phase with the same time bounds as above, we can enumerate the respective classes efficiently. For example, after $O(2^nn^4)$ time of preprocessing we can enumerate the set of all crossing-free perfect matchings using polynomial time per enumerated object. For crossing-free perfect matchings and convex partitions we further obtain enumeration algorithms where the time delay for each (in particular, the first) output is bounded by a polynomial in $n$.</p><p>All described algorithms are comparatively simple, both in terms of their analysis and implementation.</p>2017-04-25T09:51:07-04:00Copyright (c) 2017 Journal of Computational Geometry