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A Spectral Approach to Polytope Diameter Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-03-16 Hariharan Narayanan, Rikhav Shah, Nikhil Srivastava
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(Re)packing Equal Disks into Rectangle Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-03-12 Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, Meirav Zehavi
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Decomposing the Complement of the Union of Cubes and Boxes in Three Dimensions Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-03-02
Abstract Let \(\mathcal {C}\) be a set of n axis-aligned cubes of arbitrary sizes in \({\mathbb R}^3\) in general position. Let \(\mathcal {U}:=\mathcal {U}(\mathcal {C})\) be their union, and let \(\kappa \) be the number of vertices on \(\partial \mathcal {U}\) ; \(\kappa \) can vary between O(1) and \(\Theta (n^2)\) . We present a partition of \(\mathop {\textrm{cl}}({\mathbb R}^3\setminus \mathcal
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On Compact Packings of Euclidean Space with Spheres of Finitely Many Sizes Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-22 Miek Messerschmidt, Eder Kikianty
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Total Cut Complexes of Graphs Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-22 Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Rowan Rowlands, Sheila Sundaram, Lei Xue
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Efficient Computation of a Semi-Algebraic Basis of the First Homology Group of a Semi-Algebraic Set Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-22 Saugata Basu, Sarah Percival
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Computing the Homology Functor on Semi-algebraic Maps and Diagrams Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-14 Saugata Basu, Negin Karisani
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Convexity, Elementary Methods, and Distances Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-03 Oliver Roche-Newton, Dmitrii Zhelezov
This paper considers an extremal version of the Erdős distinct distances problem. For a point set \(P \subset {\mathbb {R}}^d\), let \(\Delta (P)\) denote the set of all Euclidean distances determined by P. Our main result is the following: if \(\Delta (A^d) \ll |A|^2\) and \(d \ge 5\), then there exists \(A' \subset A\) with \(|A'| \ge |A|/2\) such that \(|A'-A'| \ll |A| \log |A|\). This is one part
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Locally Finite Completions of Polyhedral Complexes Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-03 Desmond Coles, Netanel Friedenberg
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Peeling Sequences Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-02-02 Adrian Dumitrescu, Géza Tóth
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Computable Bounds for the Reach and r-Convexity of Subsets of $${{\mathbb {R}}}^d$$ Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-27 Ryan Cotsakis
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The Cone of $$5\times 5$$ Completely Positive Matrices Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-24 Max Pfeffer, José Alejandro Samper
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Almost Congruent Triangles Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-11
Abstract Almost 50 years ago Erdős and Purdy asked the following question: Given n points in the plane, how many triangles can be approximate congruent to equilateral triangles? They pointed out that by dividing the points evenly into three small clusters built around the three vertices of a fixed equilateral triangle, one gets at least \(\left\lfloor \frac{n}{3} \right\rfloor \cdot \left\lfloor \frac{n+1}{3}
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Euclidean TSP in Narrow Strips Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-08 Henk Alkema, Mark de Berg, Remco van der Hofstad, Sándor Kisfaludi-Bak
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Counting Arcs in $${\mathbb {F}}_q^2$$ Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-08 Krishnendu Bhowmick, Oliver Roche-Newton
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Topological Optimization with Big Steps Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-05 Arnur Nigmetov, Dmitriy Morozov
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Plurality in Spatial Voting Games with Constant $$\beta $$ Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-03 Arnold Filtser, Omrit Filtser
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Dynamic Connectivity in Disk Graphs Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-03 Alexander Baumann, Haim Kaplan, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, Paul Seiferth
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Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs Discret. Comput. Geom. (IF 0.8) Pub Date : 2024-01-03 Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, Alexandra Weinberger
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When is a Planar Rod Configuration Infinitesimally Rigid? Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-19 Signe Lundqvist, Klara Stokes, Lars-Daniel Öhman
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Deep Cliques in Point Sets Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-18 Stefan Langerman, Marcelo Mydlarz, Emo Welzl
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Restricted Birkhoff Polytopes and Ehrhart Period Collapse Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-16 Per Alexandersson, Sam Hopkins, Gjergji Zaimi
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the “longest increasing subsequence” have Ehrhart quasi-polynomials which are honest polynomials, even though they are just rational polytopes in general. We do this by defining a continuous, piecewise-linear bijection to a certain Gelfand–Tsetlin polytope. This bijection is not an integral
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Orthogonal Dissection into Few Rectangles Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-12 David Eppstein
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Improved Estimates on the Number of Unit Perimeter Triangles Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-09 Ritesh Goenka, Kenneth Moore, Ethan Patrick White
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The Parameterized Complexity of Guarding Almost Convex Polygons Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-12-05 Akanksha Agrawal, Kristine V. K. Knudsen, Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi
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Furstenberg Sets in Finite Fields: Explaining and Improving the Ellenberg–Erman Proof Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-29 Manik Dhar, Zeev Dvir, Ben Lund
A (k, m)-Furstenberg set is a subset \(S \subset {\mathbb {F}}_q^n\) with the property that each k-dimensional subspace of \({\mathbb {F}}_q^n\) can be translated so that it intersects S in at least m points. Ellenberg and Erman (Algebra Number Theory 10(7), 1415–1436 (2016)) proved that (k, m)-Furstenberg sets must have size at least \(C_{n,k}m^{n/k}\), where \(C_{n,k}\) is a constant depending only
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Geometric Stabbing via Threshold Rounding and Factor Revealing LPs Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-27 Khaled Elbassioni, Saurabh Ray
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Ehrhart Quasi-Polynomials of Almost Integral Polytopes Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-24 Christopher de Vries, Masahiko Yoshinaga
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Trilateration Using Unlabeled Path or Loop Lengths Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-25 Ioannis Gkioulekas, Steven J. Gortler, Louis Theran, Todd Zickler
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Volumes of Subset Minkowski Sums and the Lyusternik Region Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-21 Franck Barthe, Mokshay Madiman
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Some New Results on Geometric Transversals Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-16 Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
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Grounded L-Graphs Are Polynomially $$\chi $$ -Bounded Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-16 James Davies, Tomasz Krawczyk, Rose McCarty, Bartosz Walczak
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Discrete Morse Theory for Computing Zigzag Persistence Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-15 Clément Maria, Hannah Schreiber
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Distortion Reversal in Aperiodic Tilings Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-14 Louisa Barnsley, Michael Barnsley, Andrew Vince
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Spiraling and Folding: The Topological View Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-12 Jan Kynčl, Marcus Schaefer, Eric Sedgwick, Daniel Štefankovič
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Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-07 Taylor Brysiewicz, Holger Eble, Lukas Kühne
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An $$\mathcal {O}(3.82^{k})$$ Time $$\textsf {FPT}$$ Algorithm for Convex Flip Distance Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-05 Haohong Li, Ge Xia
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On the Structure of Pointsets with Many Collinear Triples Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-02 József Solymosi
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Short Topological Decompositions of Non-orientable Surfaces Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-01 Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay
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A Topology-Shape-Metrics Framework for Ortho-Radial Graph Drawing Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-11-01 Lukas Barth, Benjamin Niedermann, Ignaz Rutter, Matthias Wolf
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The Limit of $$L_p$$ Voronoi Diagrams as $$p\rightarrow 0$$ is the Bounding-Box-Area Voronoi Diagram Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-26 Herman Haverkort, Rolf Klein
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On Semialgebraic Range Reporting Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-24 Peyman Afshani, Pingan Cheng
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Matroids of Gain Signed Graphs Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-21 Laura Anderson, Ting Su, Thomas Zaslavsky
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$$\varepsilon $$ -Isometric Dimension Reduction for Incompressible Subsets of $$\ell _p$$ Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-21 Alexandros Eskenazis
Fix \(p\in [1,\infty )\), \(K\in (0,\infty )\), and a probability measure \(\mu \). We prove that for every \(n\in \mathbb {N}\), \(\varepsilon \in (0,1)\), and \(x_1,\ldots ,x_n\in L_p(\mu )\) with \(\big \Vert \max _{i\in \{1,\ldots ,n\}} |x_i| \big \Vert _{L_p(\mu )} \le K\), there exist \(d\le \frac{32e^2 (2K)^{2p}\log n}{\varepsilon ^2}\) and vectors \(y_1,\ldots , y_n \in \ell _p^d\) such that
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Pizza and 2-Structures Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-17 Richard Ehrenborg, Sophie Morel, Margaret Readdy
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Adjacency Graphs of Polyhedral Surfaces Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-18 Elena Arseneva, Linda Kleist, Boris Klemz, Maarten Löffler, André Schulz, Birgit Vogtenhuber, Alexander Wolff
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Inscribable Order Types Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-18 Michael Gene Dobbins, Seunghun Lee
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An Identity for the Coefficients of Characteristic Polynomials of Hyperplane Arrangements Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-18 Zakhar Kabluchko
Consider a finite collection of affine hyperplanes in \(\mathbb R^d\). The hyperplanes dissect \(\mathbb R^d\) into finitely many polyhedral chambers. For a point \(x\in \mathbb R^d\) and a chamber P the metric projection of x onto P is the unique point \(y\in P\) minimizing the Euclidean distance to x. The metric projection is contained in the relative interior of a uniquely defined face of P whose
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Evasive Sets, Covering by Subspaces, and Point-Hyperplane Incidences Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-17 Benny Sudakov, István Tomon
Given positive integers \(k\le d\) and a finite field \(\mathbb {F}\), a set \(S\subset \mathbb {F}^{d}\) is (k, c)-subspace evasive if every k-dimensional affine subspace contains at most c elements of S. By a simple averaging argument, the maximum size of a (k, c)-subspace evasive set is at most \(c |\mathbb {F}|^{d-k}\). When k and d are fixed, and c is sufficiently large, the matching lower bound
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Embeddings of k-Complexes into 2k-Manifolds Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-16 Pavel Paták, Martin Tancer
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Lower Bound on Translative Covering Density of Tetrahedra Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-16 Yiming Li, Miao Fu, Yuqin Zhang
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Deformed Graphical Zonotopes Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-13 Arnau Padrol, Vincent Pilaud, Germain Poullot
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Tropical Compactification via Ganter’s Algorithm Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-14 Lars Kastner, Kris Shaw, Anna-Lena Winz
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The VC-Dimension and Point Configurations in $${\mathbb F}_q^2$$ Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-10 David Fitzpatrick, Alex Iosevich, Brian McDonald, Emmett Wyman
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Extracting Persistent Clusters in Dynamic Data via Möbius Inversion Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-11 Woojin Kim, Facundo Mémoli
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Periodic Steiner Networks Minimizing Length Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-09 Jerome Alex, Karsten Grosse-Brauckmann
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Approximating Maximum Integral Multiflows on Bounded Genus Graphs Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-09 Chien-Chung Huang, Mathieu Mari, Claire Mathieu, Jens Vygen
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Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and Its Applications Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-07 Tamal K. Dey, Woojin Kim, Facundo Mémoli
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The Ultrametric Gromov–Wasserstein Distance Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-07 Facundo Mémoli, Axel Munk, Zhengchao Wan, Christoph Weitkamp
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On the Spanning and Routing Ratio of the Directed Theta-Four Graph Discret. Comput. Geom. (IF 0.8) Pub Date : 2023-10-06 Prosenjit Bose, Jean-Lou De Carufel, Darryl Hill, Michiel Smid