当前期刊: Discrete & Computational Geometry Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • A Spanner for the Day After
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-08-06
    Kevin Buchin, Sariel Har-Peled, Dániel Oláh

    We show how to construct a \((1+\varepsilon )\)-spanner over a set \({P}\) of n points in \({\mathbb {R}}^d\) that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters \({\vartheta },\varepsilon \in (0,1)\), the computed spanner \({G}\) has $$\begin{aligned} {{\mathcal {O}}}\bigl (\varepsilon ^{-O(d)} {\vartheta }^{-6} n(\log \log n)^6 \log n \bigr ) \end{aligned}$$

    更新日期:2020-08-06
  • A Fast Shortest Path Algorithm on Terrain-like Graphs
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-08-04
    Vincent Froese, Malte Renken

    Terrain visibility graphs are a well-known graph class in computational geometry. They are closely related to polygon visibility graphs, but a precise graph-theoretical characterization is still unknown. Over the last decade, terrain visibility graphs attracted considerable attention in the context of time series analysis (there called time series visibility graphs) with various practical applications

    更新日期:2020-08-05
  • Computing the Fréchet Gap Distance
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-08-03
    Chenglin Fan, Benjamin Raichel

    Measuring the similarity of two polygonal curves is a fundamental computational task. Among alternatives, the Fréchet distance is one of the most well-studied similarity measures. Informally, the Fréchet distance is described as the minimum leash length required for a man on one of the curves to walk a dog on the other curve continuously from the starting to the ending points. In this paper we study

    更新日期:2020-08-03
  • On Grids in Point-Line Arrangements in the Plane
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-29
    Mozhgan Mirzaei, Andrew Suk

    The famous Szemerédi–Trotter theorem states that any arrangement of n points and n lines in the plane determines \(O(n^{4/3})\) incidences, and this bound is tight. In this paper, we prove the following Turán-type result for point-line incidence. Let \(\mathcal {L}_a\) and \(\mathcal {L}_b\) be two sets of t lines in the plane and let \(P=\{\ell _a \cap \ell _b : \ell _a \in \mathcal {L}_a, \,\ell

    更新日期:2020-07-29
  • Dynamic Geometric Data Structures via Shallow Cuttings
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-24
    Timothy M. Chan

    We present new results on a number of fundamental problems about dynamic geometric data structures: (1) We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest empty circle for a 2D point set, (iii) the Hausdorff distance between two 2D point sets, (iv) the

    更新日期:2020-07-24
  • Reconstruction of Convex Bodies from Moments
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-22
    Astrid Kousholt, Julia Schulte

    We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result

    更新日期:2020-07-23
  • On the Number of Perfect Triangles with a Fixed Angle
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-20
    Mehdi Makhul

    Richard Guy asked the following question: can we find a triangle with rational sides, medians and area? Such a triangle is called a perfect triangle and no example has been found to date. It is widely believed that such a triangle does not exist. Here we use the setup of Solymosi and de Zeeuw about rational distance sets contained in an algebraic curve, to show that for any angle \(0<\theta < \pi \)

    更新日期:2020-07-20
  • Eliminating Depth Cycles Among Triangles in Three Dimensions
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-14
    Boris Aronov, Edward Y. Miller, Micha Sharir

    The vertical depth relation among n pairwise openly disjoint triangles in 3-space may contain cycles. We show that, for any \(\varepsilon >0\), the triangles can be cut into \(O(n^{3/2+\varepsilon })\) connected semialgebraic pieces, whose description complexity depends only on the choice of \(\varepsilon \), such that the depth relation among these pieces is now a proper partial order. This bound

    更新日期:2020-07-14
  • On Weak $$\epsilon $$ ϵ -Nets and the Radon Number
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-13
    Shay Moran, Amir Yehudayoff

    We show that the Radon number characterizes the existence of weak nets in separable convexity spaces (an abstraction of the Euclidean notion of convexity). The construction of weak nets when the Radon number is finite is based on Helly’s property and on metric properties of VC classes. The lower bound on the size of weak nets when the Radon number is large relies on the chromatic number of the Kneser

    更新日期:2020-07-13
  • On the Number of Weakly Connected Subdigraphs in Random k NN Digraphs
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-06
    Selim Bahadır, Elvan Ceyhan

    We study the number of copies of a weakly connected subdigraph of the k nearest neighbor (kNN) digraph based on data from certain random point processes in \(\mathbb {R}^d\). In particular, based on the asymptotic theory for functionals of point sets from homogeneous Poisson process (HPP) and uniform binomial process (UBP), we provide a general result for the asymptotic behavior of the number of weakly

    更新日期:2020-07-06
  • Computing Min-Convex Hulls in the Affine Building of $$\hbox {SL}_d$$ SL d
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-06
    Leon Zhang

    We describe an algorithm for computing the min-convex hull of a finite collection of points in the affine building of \(\hbox {SL}_d(K)\), for K a field with discrete valuation. These min-convex hulls describe the relations among a finite collection of invertible matrices over K. As a consequence, we bound the dimension of the tropical projective space needed to realize the min-convex hull as a tropical

    更新日期:2020-07-06
  • Finding Needles in a Haystack
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-06
    Árpád Kurusa

    Convex polygons are distinguishable among the piecewise \(C^\infty \) convex domains by comparing their visual angle functions on any surrounding circle. This is a consequence of our main result, that every segment in a \(C^\infty \) multicurve can be reconstructed from the masking function of the multicurve given on any surrounding circle.

    更新日期:2020-07-06
  • The Graphs Behind Reuleaux Polyhedra
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-07-06
    Luis Montejano, Eric Pauli, Miguel Raggi, Edgardo Roldán-Pensado

    This work is about graphs arising from Reuleaux polyhedra. Such graphs must necessarily be planar, 3-connected and strongly self-dual. We study the question of when these conditions are sufficient. If G is any such graph, each vertex has an opposite face with isomorphism \(\tau :G \rightarrow G^*\) (where \(G^*\) is the unique dual graph), a metric mapping is a map \(\eta :V(G) \rightarrow \mathbb

    更新日期:2020-07-06
  • Near-Optimal Algorithms for Shortest Paths in Weighted Unit-Disk Graphs
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-24
    Haitao Wang, Jie Xue

    We revisit a classical graph-theoretic problem, the single-source shortest-path (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in \(O(n\log ^2\!n)\) time using linear space, where n is the number of the vertices of the graph. This significantly improves the previous deterministic algorithm by Cabello and Jejčič [CGTA’15]

    更新日期:2020-06-25
  • Constructing Planar Support for Non-Piercing Regions
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-22
    Rajiv Raman, Saurabh Ray

    Given a hypergraph \(\mathcal {H}=(X,{\mathcal {S}})\), a planar support for \(\mathcal {H}\) is a planar graph G with vertex set X, such that for each hyperedge \(S\in \mathcal {S}\), the subgraph of G induced by the vertices in S is connected. Planar supports for hypergraphs have found several algorithmic applications, including several packing and covering problems, hypergraph coloring, and in hypergraph

    更新日期:2020-06-23
  • The Schläfli Fan
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-22
    Michael Joswig, Marta Panizzut, Bernd Sturmfels

    Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular secondary fan of the triple tetrahedron. There are \(344\, 843 \,867\) such cones, organized into a database of \(14\,373\,645\) symmetry classes. The Schläfli fan gives a further refinement of these cones. It reveals all possible patterns of lines on tropical cubic surfaces, thus serving as a combinatorial base space

    更新日期:2020-06-23
  • Theorems of Carathéodory, Helly, and Tverberg Without Dimension
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-19
    Karim Adiprasito, Imre Bárány, Nabil H. Mustafa, Tamás Terpai

    We initiate the study of no-dimensional versions of classical theorems in convexity. One example is Carathéodory’s theorem without dimension: given an n-element set P in a Euclidean space, a point \(a \in {{\,\mathrm{{\texttt {conv}}}\,}}P\), and an integer \(r \le n\), there is a subset \(Q\subset P\) of r elements such that the distance between a and \({{\,\mathrm{{\texttt {conv}}}\,}}Q\) is less

    更新日期:2020-06-19
  • Discrete Equidecomposability and Ehrhart Theory of Polygons
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-10
    Paxton Turner, Yuhuai Wu

    Motivated by questions from Ehrhart theory, we present new results on discrete equidecomposability. Two rational polygons P and Q are said to be discretely equidecomposable if there exists a piecewise affine-unimodular bijection (equivalently, a piecewise affine-linear bijection that preserves the integer lattice \({\mathbb {Z}}^2\)) from P to Q. We develop an invariant for a particular version of

    更新日期:2020-06-10
  • Almost All String Graphs are Intersection Graphs of Plane Convex Sets
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-05
    János Pach, Bruce Reed, Yelena Yuditsky

    A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair

    更新日期:2020-06-05
  • An Exploration of Locally Spherical Regular Hypertopes
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-03
    Maria Elisa Fernandes, Dimitri Leemans, Asia Ivić Weiss

    Hypertope is a generalization of the concept of polytope, which in turn generalizes the concept of a map and hypermap, to higher rank objects. Regular hypertopes with spherical residues, which we call regular locally spherical hypertopes, must be either of spherical, euclidean, or hyperbolic type. That is, the type-preserving automorphism group of a locally spherical regular hypertope is a quotient

    更新日期:2020-06-03
  • Intersection Patterns of Planar Sets
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-06-02
    Gil Kalai, Zuzana Patáková

    Let \({\mathcal {A}}=\{A_1,\ldots ,A_n\}\) be a family of sets in the plane. For \(0 \le i < n\), denote by \(f_i\) the number of subsets \(\sigma \) of \(\{1,\ldots ,n\}\) of cardinality \(i+1\) that satisfy \(\bigcap _{i \in \sigma } A_i \ne \emptyset \). Let \(k \ge 2\) be an integer. We prove that if each k-wise and \((k{+}1)\)-wise intersection of sets from \({\mathcal {A}}\) is empty, or a single

    更新日期:2020-06-02
  • Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-05-29
    Adam Brown, Bei Wang

    We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the

    更新日期:2020-05-29
  • On the Number of Monochromatic Lines in $$\pmb {\mathbb {R}}^d$$Rd
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-05-27
    Mario Huicochea

    Let X be a nonempty finite subset of \({\mathbb {R}}^d\) and \(X=\bigcup _{i=1}^m X_i\) a coloring with \(m

    更新日期:2020-05-27
  • Symmetric Non-Negative Forms and Sums of Squares
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-05-21
    Grigoriy Blekherman, Cordian Riener

    We study symmetric non-negative forms and their relationship with symmetric sums of squares. For a fixed number of variables n and degree 2d, symmetric non-negative forms and symmetric sums of squares form closed, convex cones in the vector space of n-variate symmetric forms of degree 2d. Using representation theory of the symmetric group we characterize both cones in a uniform way. Further, we investigate

    更新日期:2020-05-21
  • Admissible Complexes for the Projective X-ray Transform over a Finite Field
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-05-09
    David V. Feldman, Eric L. Grinberg

    We consider the X-ray transform in a projective space over a finite field. It is well known (after Bolker) that this transform is injective. We formulate an analog of Gelfand’s admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

    更新日期:2020-05-09
  • Simple Realizability of Complete Abstract Topological Graphs Simplified
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-05-04
    Jan Kynčl

    An abstract topological graph (briefly an AT-graph) is a pair \(A=(G,{\mathcal {X}})\) where \(G=(V,E)\) is a graph and \({\mathcal {X}}\subseteq {E \atopwithdelims ()2}\) is a set of pairs of its edges. The AT-graph A is simply realizable if G can be drawn in the plane so that each pair of edges from \({\mathcal {X}}\) crosses exactly once and no other pair crosses. We show that simply realizable

    更新日期:2020-05-04
  • Correction to: On the Links of Vertices in Simplicial d -Complexes Embeddable in the Euclidean 2 d -Space
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-03-16
    Salman Parsa

    In the following we refer to the original paper [1]. The main reason for writing this correction is the incorrect statement.

    更新日期:2020-03-16
  • On Polyatomic Tomography over Abelian Groups: Some Remarks on Consistency, Tree Packings and Complexity
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-02-02
    Peter Gritzmann, Barbara Langfeld

    The paper deals with an inverse problem of reconstructing matrices from their marginal sums. More precisely, we are interested in the existence of \(r\times s\) matrices for which only the following information is available: The entries belong to known subsets of c distinguishable abelian groups, and the row and column sums of all entries from each group are given. This generalizes Ryser’s classical

    更新日期:2020-02-02
  • Treetopes and Their Graphs
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2020-01-25
    David Eppstein

    We define treetopes, a generalization of the three-dimensional roofless polyhedra (Halin graphs) to arbitrary dimensions. Like roofless polyhedra, treetopes have a designated base facet which intersects every face of dimension greater than one in more than one point. We prove an equivalent characterization of the 4-treetopes using the concept of clustered planarity from graph drawing, and we use this

    更新日期:2020-01-25
  • Decomposing Arrangements of Hyperplanes: VC-Dimension, Combinatorial Dimension, and Point Location
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-12-17
    Esther Ezra, Sariel Har-Peled, Haim Kaplan, Micha Sharir

    This work is motivated by several basic problems and techniques that rely on space decomposition of arrangements of hyperplanes in high-dimensional spaces, most notably Meiser’s 1993 algorithm (Meiser in Inf Comput 106(2):286–303, 1993) for point location in such arrangements. A standard approach to these problems is via random sampling, in which one draws a random sample of the hyperplanes, constructs

    更新日期:2019-12-17
  • Ordered and Convex Geometric Trees with Linear Extremal Function
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-11-09
    Zoltán Füredi, Alexandr Kostochka, Dhruv Mubayi, Jacques Verstraëte

    The extremal functions \(\mathrm{{ex}}_{\rightarrow }(n,F)\) and \(\mathrm{{ex}}_{\circlearrowright }(n,F)\) for ordered and convex geometric acyclic graphs F have been extensively investigated by a number of researchers. Basic questions are to determine when \(\mathrm{{ex}}_{\rightarrow }(n,F)\) and \(\mathrm{{ex}}_{\circlearrowright }(n,F)\) are linear in n, the latter posed by Brass–Károlyi–Valtr

    更新日期:2019-11-09
  • On open and closed convex codes.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2018-12-13
    Joshua Cruz,Chad Giusti,Vladimir Itskov,Bill Kronholm

    Neural codes serve as a language for neurons in the brain. Open (or closed) convex codes, which arise from the pattern of intersections of collections of open (or closed) convex sets in Euclidean space, are of particular relevance to neuroscience. Not every code is open or closed convex, however, and the combinatorial properties of a code that determine its realization by such sets are still poorly

    更新日期:2019-11-01
  • On Sets Defining Few Ordinary Circles.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2017-12-30
    Aaron Lin,Mehdi Makhul,Hossein Nassajian Mojarrad,Josef Schicho,Konrad Swanepoel,Frank de Zeeuw

    An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least [Formula: see text] ordinary circles. Moreover, we determine the exact minimum number of ordinary circles for all sufficiently large n and describe all point sets that come close to this minimum. We also

    更新日期:2019-11-01
  • On the Densest Packing of Polycylinders in Any Dimension.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2016-04-14
    Wöden Kusner

    Using transversality and a dimension reduction argument, a result of Bezdek and Kuperberg is applied to polycylinders, showing that the optimal packing density of [Formula: see text] equals [Formula: see text] for all natural numbers n.

    更新日期:2019-11-01
  • Liftings and stresses for planar periodic frameworks.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2016-03-15
    Ciprian Borcea,Ileana Streinu

    We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for their finite counterparts. These properties are then applied to questions originating

    更新日期:2019-11-01
  • Gain-Sparsity and Symmetry-Forced Rigidity in the Plane.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2016-02-24
    Tibor Jordán,Viktória E Kaszanitzky,Shin-Ichi Tanigawa

    We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2k with odd k, unifying and extending previous work on this subject. We also explore the

    更新日期:2019-11-01
  • Coloring [Formula: see text]-Embeddable [Formula: see text]-Uniform Hypergraphs.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2014-11-25
    Carl Georg Heise,Konstantinos Panagiotou,Oleg Pikhurko,Anusch Taraz

    This paper extends the scenario of the Four Color Theorem in the following way. Let [Formula: see text] be the set of all [Formula: see text]-uniform hypergraphs that can be (linearly) embedded into [Formula: see text]. We investigate lower and upper bounds on the maximum (weak) chromatic number of hypergraphs in [Formula: see text]. For example, we can prove that for [Formula: see text] there are

    更新日期:2019-11-01
  • Reconstruction Using Witness Complexes.
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2008-10-01
    Leonidas J Guibas,Steve Y Oudot

    We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to Chew's surface meshing algorithm, with one notable difference though: the restricted Delaunay triangulation is replaced by the witness complex, which makes our

    更新日期:2019-11-01
  • Poisson-Delaunay Mosaics of Order k.
    Discret. Comput. Geom. (IF 0.621) Pub Date : null
    Herbert Edelsbrunner,Anton Nikitenko

    The order-k Voronoi tessellation of a locally finite set X ⊆ R n decomposes R n into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by

    更新日期:2019-11-01
  • Barcodes of Towers and a Streaming Algorithm for Persistent Homology.
    Discret. Comput. Geom. (IF 0.621) Pub Date : null
    Michael Kerber,Hannah Schreiber

    A tower is a sequence of simplicial complexes connected by simplicial maps. We show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tower. Our approach is based on the coning strategy by Dey et al. (SoCG, 2014). We show that a variant of this approach yields a filtration that is asymptotically only marginally larger than the tower and

    更新日期:2019-11-01
  • A One-Page Solution of a Problem of Erdős and Purdy
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-10-16
    Rom Pinchasi, Alexandr Polyanskii

    The following theorem was conjectured by Erdős and Purdy: Let P be a set of \(n>4\) points in general position in the plane. Suppose that R is a set of points disjoint from P such that every line determined by P passes through a point in R. Then \(|R| \ge n\). In this paper we give a very elegant and elementary proof of this, being a very good candidate for the “book proof” of this conjecture.

    更新日期:2019-10-16
  • Complexity Yardsticks for f -Vectors of Polytopes and Spheres
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-10-10
    Eran Nevo

    We consider geometric and computational measures of complexity for sets of integer vectors, asking for a qualitative difference between f-vectors of simplicial and general d-polytopes, as well as flag f-vectors of d-polytopes and regular CW \((d-1)\)-spheres, for \(d\ge 4\).

    更新日期:2019-10-10
  • Near-Optimal Coresets of Kernel Density Estimates
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-09-25
    Jeff M. Phillips, Wai Ming Tai

    We construct near-optimal coresets for kernel density estimates for points in \({\mathbb {R}}^d\) when the kernel is positive definite. Specifically we provide a polynomial time construction for a coreset of size \(O(\sqrt{d}/\varepsilon \cdot \sqrt{\log 1/\varepsilon } )\), and we show a near-matching lower bound of size \(\Omega (\min \{\sqrt{d}/\varepsilon , 1/\varepsilon ^2\})\). When \(d\ge 1/\varepsilon

    更新日期:2019-09-25
  • Ideal Hyperbolic Polyhedra and Discrete Uniformization
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-09-05
    Boris Springborn

    We provide a constructive, variational proof of Rivin’s realization theorem for ideal hyperbolic polyhedra with prescribed intrinsic metric, which is equivalent to a discrete uniformization theorem for spheres. The same variational method is also used to prove a discrete uniformization theorem of Gu et al. and a corresponding polyhedral realization result of Fillastre. The variational principles involve

    更新日期:2019-09-05
  • Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-08-29
    Károly J. Böröczky, Máté Matolcsi, Imre Z. Ruzsa, Francisco Santos, Oriol Serra

    For a set A of points in the plane, not all collinear, we denote by \({\mathrm{tr}}(A)\) the number of triangles in a triangulation of A, that is, \({\mathrm{tr}}(A)=2i+b-2\), where b and i are the numbers of boundary and interior points of the convex hull [A] of A respectively. We conjecture the following discrete analog of the Brunn–Minkowski inequality: for any two finite point sets \(A,B\subset

    更新日期:2019-08-29
  • Capacitated Covering Problems in Geometric Spaces
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-08-29
    Sayan Bandyapadhyay, Santanu Bhowmick, Tanmay Inamdar, Kasturi Varadarajan

    We consider the following capacitated covering problem. We are given a set P of n points and a set \({\mathcal {B}}\) of balls from some metric space, and a positive integer U that represents the capacity of each of the balls in \({\mathcal {B}}\). We would like to compute a subset \({\mathcal {B}}' \subseteq {\mathcal {B}}\) of balls and assign each point in P to some ball in \({\mathcal {B}}'\) that

    更新日期:2019-08-29
  • Embeddability of Arrangements of Pseudocircles and Graphs on Surfaces
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-08-23
    Éric Colin de Verdière, Carolina Medina, Edgardo Roldán-Pensado, Gelasio Salazar

    A pseudocircle is a simple closed curve on some surface; an arrangement of pseudocircles is a collection of pseudocircles that pairwise intersect in exactly two points, at which they cross. Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most four are embeddable into the sphere, and asked if an analogous result holds

    更新日期:2019-08-23
  • The Assembly Problem for Alternating Semiregular Polytopes
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-08-14
    Barry Monson, Egon Schulte

    In the classical setting, a convex polytope is called semiregular if its facets are regular and its symmetry group is transitive on vertices. This paper continues our study of alternating abstract semiregular polytopes \(\mathcal {S}\). These structures have two kinds of abstract regular facets \(\mathcal {P}\) and \(\mathcal {Q}\), still with combinatorial automorphism group transitive on vertices

    更新日期:2019-08-14
  • Plus Minus Analogues for Affine Tverberg Type Results
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-08-01
    Pavle V. M. Blagojević, Günter M. Ziegler

    The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex and computational geometry as well as a testing ground for methods from equivariant algebraic topology. In 2018, Bárány and Soberón presented a new variation, the “Tverberg plus minus theorem.” In this paper, we give a new proof of the Tverberg plus minus

    更新日期:2019-08-01
  • On Regular Polytopes of 2-Power Order
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-07-31
    Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans

    For each \(d\ge 3\), \(n \ge 5\), and \(k_1, k_2, \ldots , k_{d-1}\ge 2\) with \(k_1+k_2+\cdots +k_{d-1}\le n-1\), we show how to construct a regular d-polytope whose automorphism group is of order \(2^n\) and whose Schläfli type is \(\{2^{k_1},2^{k_2}, \ldots , 2^{k_{d-1}}\}\).

    更新日期:2019-07-31
  • Tree Drawings Revisited
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-06-05
    Timothy M. Chan

    We make progress on a number of open problems concerning the area requirement for drawing trees on a grid. We prove that (1) every tree of size n (with arbitrarily large degree) has a straight-line drawing with area \(n2^{O(\sqrt{\log \log n\log \log \log n})}\), improving the longstanding \(O(n\log n)\) bound; (2) every tree of size n (with arbitrarily large degree) has a straight-line upward drawing

    更新日期:2019-06-05
  • Further Consequences of the Colorful Helly Hypothesis
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-05-06
    Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado, Natan Rubin

    Let \(\mathcal {F}\) be a family of convex sets in \({\mathbb {R}}^d,\) which are colored with \(d+1\) colors. We say that \(\mathcal {F}\) satisfies the Colorful Helly Property if every rainbow selection of \(d+1\) sets, one set from each color class, has a non-empty common intersection. The Colorful Helly Theorem of Lovász states that for any such colorful family \(\mathcal {F}\) there is a color

    更新日期:2019-05-06
  • The Chromatic Number of the Plane is At Least 5: A New Proof
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2019-01-22
    Geoffrey Exoo, Dan Ismailescu

    We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points one unit apart which are identically colored.

    更新日期:2019-01-22
  • A Crossing Lemma for Multigraphs
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2018-12-19
    János Pach, Géza Tóth

    Let G be a drawing of a graph with n vertices and \(e>4n\) edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvátal, Newborn, Szemerédi and Leighton, the number of crossings in G is at least \(c\,{e^3\over n^2}\), for a suitable constant \(c>0\). In a seminal paper, Székely generalized this result

    更新日期:2018-12-19
  • Polytopes Close to Being Simple
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2018-12-19
    Guillermo Pineda-Villavicencio, Julien Ugon, David Yost

    It is known that polytopes with at most two nonsimple vertices are reconstructible from their graphs, and that d-polytopes with at most \(d-2\) nonsimple vertices are reconstructible from their 2-skeletons. Here we close the gap between 2 and \(d-2\), showing that certain polytopes with more than two nonsimple vertices are reconstructible from their graphs. In particular, we prove that reconstructibility

    更新日期:2018-12-19
  • From a ( p , 2)-Theorem to a Tight ( p , q )-Theorem
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2018-11-27
    Chaya Keller, Shakhar Smorodinsky

    A family \(\mathcal {F}\) of sets is said to satisfy the (p, q)-property if among any p sets of \(\mathcal {F}\) some q have a non-empty intersection. The celebrated (p, q)-theorem of Alon and Kleitman asserts that any family of compact convex sets in \(\mathbb {R}^d\) that satisfies the (p, q)-property for some \(q \ge d+1\), can be pierced by a fixed number (independent of the size of the family)

    更新日期:2018-11-27
  • Characterizing Face and Flag Vector Pairs for Polytopes
    Discret. Comput. Geom. (IF 0.621) Pub Date : 2018-11-09
    Hannah Sjöberg, Günter M. Ziegler

    Grünbaum, Barnette, and Reay in 1974 completed the characterization of the pairs \((f_i,f_j)\) of face numbers of 4-dimensional polytopes. Here we obtain a complete characterization of the pairs of flag numbers \((f_0,f_{03})\) for 4-polytopes. Furthermore, we describe the pairs of face numbers \((f_0,f_{d-1})\) for d-polytopes; this description is complete for even \(d\ge 6\) except for finitely many

    更新日期:2018-11-09
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
欢迎访问IOP中国网站
自然职场线上招聘会
GIANT
产业、创新与基础设施
自然科研线上培训服务
材料学研究精选
胸腔和胸部成像专题
屿渡论文,编辑服务
何川
苏昭铭
陈刚
姜涛
李闯创
李刚
北大
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
上海纽约大学
陈芬儿
厦门大学
何振宇
史大永
吉林大学
卓春祥
张昊
杨中悦
试剂库存
down
wechat
bug