Computational Geometry-Theory and Applications最新文献_第2页

An analytical representation of the 2d generalized balanced power diagram 二维广义平衡功率图的分析表示法

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-04-17 DOI: 10.1016/j.comgeo.2024.102101

Christian Jung, Claudia Redenbach

引用次数: 0

An exact algorithm for the Euclidean k-Steiner tree problem 欧氏 k-Steiner 树问题的精确算法

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-04-09 DOI: 10.1016/j.comgeo.2024.102099

Marcus Brazil , Michael Hendriksen , Jae Lee , Michael S. Payne , Charl Ras , Doreen Thomas

{"title":"An exact algorithm for the Euclidean k-Steiner tree problem","authors":"Marcus Brazil , Michael Hendriksen , Jae Lee , Michael S. Payne , Charl Ras , Doreen Thomas","doi":"10.1016/j.comgeo.2024.102099","DOIUrl":"https://doi.org/10.1016/j.comgeo.2024.102099","url":null,"abstract":"<div>The Euclidean k-Steiner tree problem asks for a minimum-cost network connecting n given points in the plane, allowing at most k additional nodes referred to as Steiner points. In the classical Steiner tree problem in which there is no restriction on the number of nodes, every Steiner point must be of degree 3. The k-Steiner problem differs in that Steiner points of degree 4 may be included in an optimal solution. This simple change leads to a number of complexities when attempting to create a generation algorithm for optimal k-Steiner trees, which has proven to be a powerful component of the flagship algorithm, namely GeoSteiner, for solving the classical Steiner tree problem. In the present paper we firstly extend the basic framework of GeoSteiner's generation algorithm to include degree-4 Steiner points. We then introduce a number of novel results restricting the structural and geometric properties of optimal k-Steiner trees, and then show how these properties may be used as topological pruning methods underpinning our generation algorithm. Finally, we present experimental data to show the effectiveness of our pruning methods in reducing the number of sub-optimal solution topologies.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S092577212400021X/pdfft?md5=e2fe47e64b9ad0273f7021d80587df58&pid=1-s2.0-S092577212400021X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140555528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Panel-point model for rigidity and flexibility analysis of rigid origami 用于刚性折纸刚度和柔度分析的面板点模型

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-04-05 DOI: 10.1016/j.comgeo.2024.102100

Kentaro Hayakawa , Zeyuan He , Simon D. Guest

{"title":"Panel-point model for rigidity and flexibility analysis of rigid origami","authors":"Kentaro Hayakawa , Zeyuan He , Simon D. Guest","doi":"10.1016/j.comgeo.2024.102100","DOIUrl":"https://doi.org/10.1016/j.comgeo.2024.102100","url":null,"abstract":"<div>In this study, we lay the groundwork for a systematic investigation of the rigidity and flexibility of rigid origami by using the mathematical model referred to as the panel-point model. Rigid origami is commonly known as a type of panel-hinge structure where rigid polygonal panels are connected by rotational hinges, and its motion and stability are often investigated from the perspective of its consistency constraints representing the rigidity and connection conditions of panels. In the proposed methodology, vertex coordinates are directly treated as the variables to represent the rigid origami in the panel-point model, and these variables are constrained by the conditions for the out-of-plane and in-plane rigidity of panels. This model offers several advantages including: 1) the simplicity of polynomial consistency constraints; 2) the ease of incorporating displacement boundary conditions; and 3) the straightforwardness of numerical simulation and visualization. It is anticipated that the presented theories in this article are valuable to a broad audience, including mathematicians, engineers, and architects.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140555529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Maximum-width rainbow-bisecting empty annulus 最大宽度彩虹分光空环

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-03-06 DOI: 10.1016/j.comgeo.2024.102088

Sang Won Bae , Sandip Banerjee , Arpita Baral , Priya Ranjan Sinha Mahapatra , Sang Duk Yoon

{"title":"Maximum-width rainbow-bisecting empty annulus","authors":"Sang Won Bae , Sandip Banerjee , Arpita Baral , Priya Ranjan Sinha Mahapatra , Sang Duk Yoon","doi":"10.1016/j.comgeo.2024.102088","DOIUrl":"https://doi.org/10.1016/j.comgeo.2024.102088","url":null,"abstract":"<div>Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in <math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> time using <math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> space, in <math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> time using <math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> space and in <math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> time using <math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> space respectively.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140113725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hierarchical categories in colored searching 彩色搜索中的层次类别

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-03-04 DOI: 10.1016/j.comgeo.2024.102090

Peyman Afshani , Rasmus Killmann , Kasper G. Larsen

{"title":"Hierarchical categories in colored searching","authors":"Peyman Afshani , Rasmus Killmann , Kasper G. Larsen","doi":"10.1016/j.comgeo.2024.102090","DOIUrl":"10.1016/j.comgeo.2024.102090","url":null,"abstract":"<div>In colored range counting (CRC), the input is a set of points where each point is assigned a “color” (or a “category”) and the goal is to store them in a data structure such that the number of distinct categories inside a given query range can be counted efficiently. CRC has strong motivations as it allows data structure to deal with categorical data.However, colors (i.e., the categories) in the CRC problem do not have any internal structure, whereas this is not the case for many datasets in practice where hierarchical categories exist or where a single input belongs to multiple categories. Motivated by these, we consider variants of the problem where such structures can be represented. We define two variants of the problem called hierarchical range counting (HCC) and sub-category colored range counting (SCRC) and consider hierarchical structures that can either be a DAG or a tree. We show that the two problems on some special trees are in fact equivalent to other well-known problems in the literature. Based on these, we also give efficient data structures when the underlying hierarchy can be represented as a tree. We show a conditional lower bound for the general case when the existing hierarchy can be any DAG, through a reduction from the orthogonal vectors problem.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0925772124000129/pdfft?md5=58168aae21edfa03ea4bb23171502329&pid=1-s2.0-S0925772124000129-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140056725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Accelerating iterated persistent homology computations with warm starts 用热启动加速迭代持续同源计算

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-03-01 DOI: 10.1016/j.comgeo.2024.102089

Yuan Luo , Bradley J. Nelson

引用次数: 0

Topological regularization via persistence-sensitive optimization 通过持久性敏感优化实现拓扑正则化

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-02-28 DOI: 10.1016/j.comgeo.2024.102086

Arnur Nigmetov , Aditi Krishnapriyan , Nicole Sanderson , Dmitriy Morozov

{"title":"Topological regularization via persistence-sensitive optimization","authors":"Arnur Nigmetov , Aditi Krishnapriyan , Nicole Sanderson , Dmitriy Morozov","doi":"10.1016/j.comgeo.2024.102086","DOIUrl":"10.1016/j.comgeo.2024.102086","url":null,"abstract":"<div>Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have emerged as a way to provide a more precise and expressive control over the solution, relying on persistent homology to quantify and reduce its roughness. All such existing techniques back-propagate gradients through the persistence diagram, which is a summary of the topological features of a function. Their downside is that they provide information only at the critical points of the function. We propose a method that instead builds on persistence-sensitive simplification and translates the required changes to the persistence diagram into changes on large subsets of the domain, including both critical and regular points. This approach enables a faster and more precise topological regularization, the benefits of which we illustrate with experimental evidence.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0925772124000087/pdfft?md5=6740a147d9e195f49dbdb29746bfe080&pid=1-s2.0-S0925772124000087-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Piercing families of convex sets in the plane that avoid a certain subfamily with lines 平面中避开某线段的凸集穿孔族

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2024-02-27 DOI: 10.1016/j.comgeo.2024.102087

Daniel McGinnis

引用次数: 0

Bounds on soft rectangle packing ratios 软矩形包装率的界限

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2023-12-22 DOI: 10.1016/j.comgeo.2023.102078

Judith Brecklinghaus, Ulrich Brenner, Oliver Kiss

{"title":"Bounds on soft rectangle packing ratios","authors":"Judith Brecklinghaus, Ulrich Brenner, Oliver Kiss","doi":"10.1016/j.comgeo.2023.102078","DOIUrl":"10.1016/j.comgeo.2023.102078","url":null,"abstract":"<div>We examine rectangle packing problems where only the areas <math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of the rectangles to be packed are given while their aspect ratios may be chosen from a given interval <math><mo>[</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>γ</mi></mrow></mfrac><mo>,</mo><mi>γ</mi><mo>]</mo></math>. In particular, we ask for the smallest possible size of a rectangle R such that, under these constraints, any collection <math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of rectangle areas of total size 1 can be packed into R. As for standard square packing problems, which are contained as a special case for <math><mi>γ</mi><mo>=</mo><mn>1</mn></math>, this question leads us to three different answers, depending on whether the aspect ratio of R is given or whether we may choose it either with or without knowing the areas <math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. Generalizing known results for square packing problems, we provide upper and lower bounds for the size of R with respect to all three variants of the problem, which are tight at least for larger values of γ. Moreover, we show how to improve these bounds on the size of R if we restrict ourselves to instances where the largest element in <math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math> is bounded.</div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139025451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Erratum to: “Densest Lattice Packings of 3–Polytopes” [Computational Geometry 16 (2000) 157–186] 勘误："3-Polytopes 的最密集晶格堆积》[《计算几何》16 (2000) 157-186] 勘误

IF 0.6 4区计算机科学

Computational Geometry-Theory and Applications Pub Date : 2023-12-20 DOI: 10.1016/j.comgeo.2023.102076

Martin Henk

引用次数: 0