Latest in cs.cg

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Voronoi diagram of orthogonal polyhedra in two and three dimensionsMay 21 2019Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly useful scenario ... More
Brief Notes and History Computing in Mexico during 50 yearsMay 18 2019The history of computing in Mexico can not be thought without the name of Prof. Harold V. McIntosh (1929-2015). For almost 50 years, in Mexico he contributed to the development of computer science with wide international recognition. Approximately in ... More
Variations of largest rectangle recognition amidst a bichromatic point setMay 17 2019Classical separability problem involving multi-color point sets is an important area of study in computational geometry. In this paper, we study different separability problems for bichromatic point set P=P_r\cup P_b on a plane, where $P_r$ and $P_b$ ... More
Practical Volume Estimation by a New Annealing Schedule for Cooling Convex BodiesMay 14 2019We study the problem of estimating the volume of convex polytopes, focusing on H- and V-polytopes, as well as zonotopes. Although a lot of effort is devoted to practical algorithms for H-polytopes there is no such method for the latter two representations. ... More
Color spanning Localized queryMay 13 2019Let P be a set of n points and each of the points is colored with one of the k possible colors. We present efficient algorithms to pre-process P such that for a given query point q, we can quickly identify the smallest color spanning object of the desired ... More
Approximating a Target Surface with 1-DOF Rigid OrigamiMay 12 2019We develop some design examples for approximating a target surface at the final rigidly folded state of a developable quadrilateral creased paper, which is folded with a 1-DOF rigid folding motion from the planar state. The final rigidly folded state ... More
HLO: Half-kernel Laplacian Operator for Surface SmoothingMay 12 2019This paper presents a simple yet effective method for feature-preserving surface smoothing. Through analyzing the differential property of surfaces, we show that the conventional discrete Laplacian operator with uniform weights is not applicable to feature ... More
Efficient Algorithms for Optimal Perimeter GuardingMay 11 2019We investigate the problem of optimally assigning a large number of robots (or other types of autonomous agents) to guard the perimeters of closed 2D regions, where the perimeter of each region to be guarded may contain multiple disjoint polygonal chains. ... More
Persistent homology of the sum metricMay 10 2019Given finite metric spaces $(X, d_X)$ and $(Y, d_Y)$, we investigate the persistent homology $PH_*(X \times Y)$ of the Cartesian product $X \times Y$ equipped with the sum metric $d_X + d_Y$. Interpreting persistent homology as a module over a polynomial ... More
Delay Parameter Selection in Permutation Entropy Using Topological Data AnalysisMay 10 2019Permutation Entropy (PE) is a powerful tool for quantifying the predictability of a sequence which includes measuring the regularity of a time series. Despite its successful application in a variety of scientific domains, PE requires a judicious choice ... More
DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud RegistrationMay 10 2019We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a RANSAC procedure ... More
Coresets for Minimum Enclosing Balls over Sliding WindowsMay 09 2019\emph{Coresets} are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable ... More
Coresets for Minimum Enclosing Balls over Sliding WindowsMay 09 2019May 10 2019\emph{Coresets} are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable ... More
Computation of Circular Area and Spherical Volume Invariants via Boundary IntegralsMay 06 2019We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume integrals as line and ... More
Geometric Firefighting in the Half-planeMay 06 2019In 2006, Alberto Bressan suggested the following problem. Suppose a circular fire spreads in the Euclidean plane at unit speed. The task is to build, in real time, barrier curves to contain the fire. At each time $t$ the total length of all barriers built ... More
FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain GuardingMay 06 2019We present fixed parameter tractable algorithms for the conflict-free coloring problem on graphs. Given a graph $G=(V,E)$, \emph{conflict-free coloring} of $G$ refers to coloring a subset of $V$ such that for every vertex $v$, there is a color that is ... More
Nostalgin: Extracting 3D City Models from Historical Image DataMay 06 2019What did it feel like to walk through a city from the past? In this work, we describe Nostalgin (Nostalgia Engine), a method that can faithfully reconstruct cities from historical images. Unlike existing work in city reconstruction, we focus on the task ... More
Most vital segment barriersMay 03 2019We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital ... More
Range closest-pair search in higher dimensionsMay 03 2019Range closest-pair (RCP) search is a range-search variant of the classical closest-pair problem, which aims to store a given set $S$ of points into some space-efficient data structure such that when a query range $Q$ is specified, the closest pair in ... More
Adversarial Training with Voronoi ConstraintsMay 02 2019Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools ... More
Flip Distance to some Plane ConfigurationsMay 02 2019We study an old geometric optimization problem in the plane. Given a perfect matching $M$ on a set of $n$ points in the plane, we can transform it to a non-crossing perfect matching by a finite sequence of flip operations. The flip operation removes two ... More
Minimum Ply Covering of Points with Disks and SquaresMay 02 2019Following the seminal work of Erlebach and van Leeuwen in SODA 2008, we introduce the minimum ply covering problem. Given a set $P$ of points and a set $S$ of geometric objects, both in the plane, our goal is to find a subset $S'$ of $S$ that covers all ... More
Pseudo-Triangle Visibility Graph: Characterization and ReconstructionMay 02 2019The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices in a plane ... More
Online Circle PackingMay 02 2019We consider the online problem of packing circles into a square container. A sequence of circles has to be packed one at a time, without knowledge of the following incoming circles and without moving previously packed circles. We present an algorithm ... More
Coordinatizing Data With Lens Spaces and Persistent CohomologyMay 01 2019We introduce here a framework to construct coordinates in \emph{finite} Lens spaces for data with nontrivial 1-dimensional $\mathbb{Z}_q$ persistent cohomology, $q\geq 3$. Said coordinates are defined on an open neighborhood of the data, yet constructed ... More
A convex cover for closed unit curves has area at least 0.0975May 01 2019We combine geometric methods with numerical box search algorithm to show that the minimal area of a convex set on the plane which can cover every closed plane curve of unit length is at least 0.0975. This improves the best previous lower bound of 0.096694. ... More
Improved Algorithms for the Bichromatic Two-Center Problem for Pairs of PointsMay 01 2019We consider a bichromatic two-center problem for pairs of points. Given a set $S$ of $n$ pairs of points in the plane, for every pair, we want to assign a red color to one point and a blue color to the other, in such a way that the value $\max\{r_1,r_2\}$ ... More
Constrained Orthogonal Segment StabbingApr 30 2019Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. It is known that the problem of stabbing the line segments in $D$ with the minimum number ... More
The graphs behind Reuleaux polyhedraApr 29 2019This 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 a graph with isomorphism $\tau : ... More
Structurally optimized shellsApr 28 2019Shells, i.e., objects made of a thin layer of material following a surface, are among the most common structures in use. They are highly efficient, in terms of material required to maintain strength, but also prone to deformation and failure. We introduce ... More
Learning metrics for persistence-based summaries and applications for graph classificationApr 27 2019Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been developed to ... More
A Classification of Topological Discrepancies in Additive ManufacturingApr 27 2019Additive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The tradeoffs between ... More
Guarantees on Nearest-Neighbor Condensation heuristicsApr 27 2019The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds have been ... More
Automatic Support Removal for Additive Manufacturing Post ProcessingApr 27 2019An additive manufacturing (AM) process often produces a {\it near-net} shape that closely conforms to the intended design to be manufactured. It sometimes contains additional support structure (also called scaffolding), which has to be removed in post-processing. ... More
A Linear-Time Algorithm for Radius-Optimally Augmenting Paths in a Metric SpaceApr 26 2019Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph was solved in ... More
Truly Optimal Euclidean SpannersApr 26 2019Euclidean spanners are important geometric structures, having found numerous applications over the years. Cornerstone results in this area from the late 80s and early 90s state that for any $d$-dimensional $n$-point Euclidean space, there exists a $(1+\epsilon)$-spanner ... More
Finding Hexahedrizations for Small Quadrangulations of the SphereApr 25 2019This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is ... More
Counting the Number of Crossings in Geometric GraphsApr 24 2019A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n^2 \log n)$ algorithm to compute the number of pairs of edges that cross ... More
Efficient Nearest-Neighbor Query and Clustering of Planar CurvesApr 24 2019We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let $\mathcal{C}$ be a set of $n$ polygonal curves, each of size $m$. In the nearest-neighbor problem, the goal is to construct ... More
Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with ApplicationsApr 21 2019In 2015, Guth proved that for any set of $k$-dimensional varieties in $\mathbb{R}^d$ and for any positive integer $D$, there exists a polynomial of degree at most $D$ whose zero-set divides $\mathbb{R}^d$ into open connected "cells," so that only a small ... More
A General Neural Network Architecture for Persistence Diagrams and Graph ClassificationApr 20 2019Graph classification is a difficult problem that has drawn a lot of attention from the machine learning community over the past few years. This is mainly due to the fact that, contrarily to Euclidean vectors, the inherent complexity of graph structures ... More
Beyond Submodular MaximizationApr 19 2019Apr 23 2019While there are well-developed tools for maximizing a submodular function subject to a matroid constraint, there is much less work on the corresponding supermodular maximization problems. We develop new techniques for attacking these problems inspired ... More
Beyond Submodular MaximizationApr 19 2019While there are well-developed tools for maximizing a submodular function subject to a matroid constraint, there is much less work on the corresponding supermodular maximization problems. We develop new techniques for attacking these problems inspired ... More
Planar Point Sets Determine Many Pairwise Crossing SegmentsApr 18 2019We show that any set of $n$ points in general position in the plane determines $n^{1-o(1)}$ pairwise crossing segments. The best previously known lower bound, $\Omega\left(\sqrt n\right)$, was proved more than 25 years ago by Aronov, Erd\H os, Goddard, ... More
Advancing Through TerrainsApr 18 2019We study terrain visibility graphs, a well-known graph class closely related to polygon visibility graphs in computational geometry, for which a precise graph-theoretical characterization is still unknown. Over the last decade, terrain visibility graphs ... More
On conflict-free chromatic guarding of simple polygonsApr 18 2019We study the problem of colouring the vertices of a polygon, such that every viewer can see a unique colour. The goal is to minimize the number of colours used. This is also known as the conflict-free chromatic guarding problem with vertex guards (which ... More
3D Shape Synthesis for Conceptual Design and Optimization Using Variational AutoencodersApr 16 2019We propose a data-driven 3D shape design method that can learn a generative model from a corpus of existing designs, and use this model to produce a wide range of new designs. The approach learns an encoding of the samples in the training corpus using ... More
Persistence Curves: A canonical framework for summarizing persistence diagramsApr 16 2019Persistence diagrams are a main tool in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to be challenging as the ... More
Relation-Shape Convolutional Neural Network for Point Cloud AnalysisApr 16 2019Apr 22 2019Point cloud analysis is very challenging, as the shape implied in irregular points is difficult to capture. In this paper, we propose RS-CNN, namely, Relation-Shape Convolutional Neural Network, which extends regular grid CNN to irregular configuration ... More
Relation-Shape Convolutional Neural Network for Point Cloud AnalysisApr 16 2019Point cloud analysis is very challenging, as the shape implied in irregular points is difficult to capture. In this paper, we propose RS-CNN, namely, Relation-Shape Convolutional Neural Network, which extends regular grid CNN to irregular configuration ... More
Persistent Homology of Complex Networks for Dynamic State DetectionApr 16 2019In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale ... More
Differentiable Iterative Surface Normal EstimationApr 15 2019This paper presents an end-to-end differentiable algorithm for anisotropic surface normal estimation on unstructured point-clouds. We utilize graph neural networks to iteratively infer point weights for a plane fitting algorithm applied to local neighborhoods. ... More
A Graph Theory Approach for Regional Controllability of Boolean Cellular AutomataApr 15 2019Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining a system to reach the desired state from an initial state within a given time interval. When ... More
Computing a Minimum-Width Cubic and Hypercubic ShellApr 15 2019In this paper, we study the problem of computing a minimum-width axis-aligned cubic shell that encloses a given set of $n$ points in a three-dimensional space. A cubic shell is a closed volume between two concentric and face-parallel cubes. Prior to this ... More
On the Minimum-Area Rectangular and Square Annulus ProblemApr 15 2019In this paper, we address the minimum-area rectangular and square annulus problem, which asks a rectangular or square annulus of minimum area, either in a fixed orientation or over all orientations, that encloses a set $P$ of $n$ input points in the plane. ... More
Drawing HV-Restricted Planar GraphsApr 14 2019A strict orthogonal drawing of a graph $G=(V, E)$ in $\mathbb{R}^2$ is a drawing of $G$ such that each vertex is mapped to a distinct point and each edge is mapped to a horizontal or vertical line segment. A graph $G$ is $HV$-restricted if each of its ... More
Parallel parametric linear programming solving, and application to polyhedral computationsApr 12 2019Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.
An asymptotic combinatorial construction of 2D-sphereApr 10 2019A geometric space is constructed as the inverse limit of infinite sequence of graphs that are dual to graphs that correspond to finer and finer 2-d sphere triangulation. The conjecture is stated that the space is isomorphic to an Euclidean 2D-sphere.
Persistence-perfect discrete gradient vector fields and multi-parameter persistenceApr 10 2019The main objective of this paper is to introduce and study a notion of perfectness for discrete gradient vector fields with respect to (multi-parameter) persistent homology. As a natural generalization of usual perfectness in Morse theory for homology, ... More
A Fast and Efficient algorithm for Many-To-Many Matching of Points with Demands in One DimensionApr 09 2019Given two point sets S and T, we first study the many-to-many matching with demands problem (MMD problem). In an MMD, each point of one set must be matched to a given number of the points of the other set, and the cost of matching a point to another point ... More
Subsets and Supermajorities: Unifying Hashing-based Set Similarity SearchApr 08 2019We consider the problem of designing Locality Sensitive Filters (LSF) for set overlaps, also known as maximum inner product search on binary data. We give a simple data structure that generalizes and outperforms previous algorithms such as MinHash [J. ... More
Minimum Enclosing Ball Revisited: Stability and Sub-linear Time AlgorithmsApr 08 2019In this paper, we revisit the Minimum Enclosing Ball (MEB) problem and its robust version, MEB with outliers, in Euclidean space $\mathbb{R}^d$. Though the problem has been extensively studied before, most of the existing algorithms need at least linear ... More
Generalized Persistence Algorithm for Decomposing Multi-parameter Persistence ModulesApr 07 2019The classical persistence algorithm virtually computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological ... More
Implicit Manifold ReconstructionApr 07 2019Let ${\cal M} \subset \mathbb{R}^d$ be a compact, smooth and boundaryless manifold with dimension $m$ and unit reach. We show how to construct a function $\varphi: \mathbb{R}^d \rightarrow \mathbb{R}^{d-m}$ from a uniform $(\varepsilon,\kappa)$-sample ... More
Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spacesApr 07 2019We give an algorithm that computes a $(1+\epsilon)$-approximate Steiner forest in near-linear time $n \cdot 2^{(1/\epsilon)^{O(ddim^2)} (\log \log n)^2}$. This is a dramatic improvement upon the best previous result due to Chan et al., who gave a runtime ... More
An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace ModelApr 05 2019We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed at random. In ... More
Drawing k-linear Metro MapsApr 05 2019Schematic metro maps in practice as well as metro map layout algorithms usually adhere to an octilinear layout style with all paths composed of horizontal, vertical, and 45$^\circ$-diagonal edges. Despite growing interest in non-octilinear metro maps, ... More
Sharing a pizza: bisecting masses with two cutsApr 04 2019Assume you have a pizza consisting of four ingredients (e.g., bread, tomatoes, cheese and olives) that you want to share with your friend. You want to do this fairly, meaning that you and your friend should get the same amount of each ingredient. How ... More
Embeddings of $k$-complexes into $2k$-manifoldsApr 04 2019If $K$ is a simplicial $k$-complex, the standard van Kampen obstructions tells you whether $K$ can be embedded into $\mathbb R^{2k}$ or not (provided $k\neq 2$). We describe how the obstruction changes if we replace $\mathbb R^{2k}$ by a closed PL $2k$-manifold ... More
A Faster Algorithm for the Limited-Capacity Many-to-Many Point Matching in One DimensionApr 04 2019Given two point sets S and T on a line, we present a linear time algorithm for the limited capacity many-to-many matching between S and T which improves the previous quadratic algorithm.
A Faster Algorithm for the Limited-Capacity Many-to-Many Point Matching in One DimensionApr 04 2019Apr 17 2019Given two point sets S and T on a line, we present a linear time algorithm for the limited capacity many-to-many matching between S and T which improves the previous quadratic algorithm.
Linearly Converging Quasi Branch and Bound Algorithms for Global Rigid RegistrationApr 03 2019Apr 14 2019In recent years, several branch-and-bound (BnB) algorithms have been proposed to globally optimize rigid registration problems. In this paper, we suggest a general framework to improve upon the BnB approach, which we name Quasi BnB. Quasi BnB replaces ... More
Linearly Converging Quasi Branch and Bound Algorithms for Global Rigid RegistrationApr 03 2019In recent years, several branch-and-bound (BnB) algorithms have been proposed to globally optimize rigid registration problems. In this paper, we suggest a general framework to improve upon the BnB approach, which we name Quasi BnB. Quasi BnB replaces ... More
Internal versus external balancing in the evaluation of graph-based number typesApr 03 2019Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by restructuring the graph ... More
Internal versus external balancing in the evaluation of graph-based number typesApr 03 2019Apr 12 2019Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by restructuring the graph ... More
On Limitations of the Witness Configuration Method for Geometric Constraint Solving in CAD ModelingApr 01 2019This paper presents discussions on the limitations of the witness configuration method. These limitations have rarely been reported in previous studies. The witness configuration method is a very recent approach for geometric constraint solving, which ... More
On Limitations of the Witness Configuration Method for Geometric Constraint Solving in CAD ModelingApr 01 2019Apr 15 2019This paper presents discussions on the limitations of the witness configuration method. These limitations have rarely been reported in previous studies. The witness configuration method is a very recent approach for geometric constraint solving, which ... More
Ham-Sandwich cuts and center transversals in subspacesMar 29 2019The Ham-Sandwich theorem is a well-known result in geometry. It states that any $d$ mass distributions in $\mathbb{R}^d$ can be simultaneously bisected by a hyperplane. The result is tight, that is, there are examples of $d+1$ mass distributions that ... More
Parallelizable global conformal parameterization of simply-connected surfaces via partial weldingMar 29 2019Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data, dense 3D surface ... More
Stability analysis of kinetic orientation-based shape descriptorsMar 27 2019We study three orientation-based shape descriptors on a set of continuously moving points $P$: the first principal component, the smallest oriented bounding box and the thinnest strip. Each of these shape descriptors essentially defines a cost capturing ... More
Convexly independent subsets of Minkowski sums of convex polygonsMar 27 2019We show that there exist convex $n$-gons $P$ and $Q$ such that the largest convex polygon in the Minkowski sum $P+Q$ has size $\Theta(n\log n)$. This matches an upper bound of Tiwary.
Robust NFP generation for Nesting problemsMar 26 2019Cutting and packing problems arise in a large variety of industrial applications, where there is a need to cut pieces from a large object, or placing them inside a containers, without overlap. When the pieces or the containers have irregular outline, ... More
Differential Geometric Foundations for Power Flow ComputationsMar 26 2019This paper aims to systematically and comprehensively initiate a foundation for using concepts from computational differential geometry as instruments for power flow computing and research. At this point we focus our discussion on the static case, with ... More
Reconstruction of r-Regular Objects from Trinary ImagesMar 26 2019We study digital images of r-regular objects where a pixel is black if it is completely inside the object, white if it is completely inside the complement of the object, and grey otherwise. We call such images trinary. We discuss possible configurations ... More
Computing the Homology of Semialgebraic Sets. II: General formulasMar 26 2019We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially ... More
A Weighted Approach to the Maximum Cardinality Bipartite Matching Problem with Applications in Geometric SettingsMar 25 2019We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or $1$. Let $w \leq n$ ... More
Level-set based design of Wang tiles for modelling complex microstructuresMar 22 2019Microstructural geometry plays a critical role in a response of heterogeneous materials. Consequently, methods for generating microstructural samples are becoming an integral part of advanced numerical analyses. Here, we extend the unified framework of ... More
Rods and Rings: Soft Subdivision Planner for R^3 x S^2Mar 22 2019Mar 25 2019We consider path planning for a rigid spatial robot moving amidst polyhedral obstacles. Our robot is either a rod or a ring. Being axially-symmetric, their configuration space is R^3 x S^2 with 5 degrees of freedom (DOF). Correct, complete and practical ... More
Efficient Algorithms for Geometric Partial MatchingMar 22 2019Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in at most one ... More
Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor productsMar 21 20193D objects, modeled using Computer Aided Geometric Design tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical ... More
Z_2-genus of graphs and minimum rank of partial symmetric matricesMar 20 2019The \emph{genus} $\mathrm{g}(G)$ of a graph $G$ is the minimum $g$ such that $G$ has an embedding on the orientable surface $M_g$ of genus $g$. A drawing of a graph on a surface is \emph{independently even} if every pair of nonadjacent edges in the drawing ... More
Almost Tight Lower Bounds for Hard Cutting Problems in Embedded GraphsMar 20 2019We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut ... More
Topological Data Analysis in Information SpaceMar 20 2019Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability ... More
Topological Data Analysis in Information SpaceMar 20 2019Mar 28 2019Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability ... More
Drawing planar graphs with few segments on a polynomial gridMar 20 2019The visual complexity of a plane graph drawing is defined to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path with ... More
Dynamic Geometric Data Structures via Shallow CuttingsMar 20 2019We 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 ... More
Maintaining the Union of Unit Discs under Insertions with Near-Optimal OverheadMar 20 2019We present efficient data structures for problems on unit discs and arcs of their boundary in the plane. (i) We give an output-sensitive algorithm for the dynamic maintenance of the union of $n$ unit discs under insertions in $O(k \log^2 n)$ update time ... More
Local Versus Global Distances for Zigzag Persistence ModulesMar 20 2019This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance between two zigzag persistence modules restricted to an interval ... More
Preprocessing Ambiguous Imprecise PointsMar 19 2019Let ${R} = \{R_1, R_2, ..., R_n\}$ be a set of regions and let $ X = \{x_1, x_2, ..., x_n\}$ be an (unknown) point set with $x_i \in R_i$. Region $R_i$ represents the uncertainty region of $x_i$. We consider the following question: how fast can we establish ... More
Independent Range Sampling, Revisited AgainMar 19 2019We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$ independent random ... More