arXiv - CS - Computational Geometry最新文献_第2页

Disjoint Compatibility via Graph Classes 通过图类实现互不相容

arXiv - CS - Computational Geometry Pub Date : 2024-09-05 DOI: arxiv-2409.03579

Oswin Aichholzer, Julia Obmann, Pavel Paták, Daniel Perz, Josef Tkadlec, Birgit Vogtenhuber

引用次数: 0

Approximation Algorithms for Anchored Multiwatchman Routes 锚定多观察者航线的近似算法

arXiv - CS - Computational Geometry Pub Date : 2024-08-30 DOI: arxiv-2408.17343

Joseph S. B. Mitchell, Linh Nguyen

引用次数: 0

Best of two worlds: Cartesian sampling and volume computation for distance-constrained configuration spaces using Cayley coordinates 两全其美：使用 Cayley 坐标为距离受限的配置空间进行笛卡尔采样和体积计算

arXiv - CS - Computational Geometry Pub Date : 2024-08-29 DOI: arxiv-2408.16946

Yichi Zhang, Meera Sitharam

{"title":"Best of two worlds: Cartesian sampling and volume computation for distance-constrained configuration spaces using Cayley coordinates","authors":"Yichi Zhang, Meera Sitharam","doi":"arxiv-2408.16946","DOIUrl":"https://doi.org/arxiv-2408.16946","url":null,"abstract":"Volume calculation of configurational spaces acts as a vital part in\u0000configurational entropy calculation, which contributes towards calculating free\u0000energy landscape for molecular systems. In this article, we present our\u0000sampling-based volume computation method using distance-based Cayley\u0000coordinate, mitigating drawbacks: our method guarantees that the sampling\u0000procedure stays in lower-dimensional coordinate space (instead of\u0000higher-dimensional Cartesian space) throughout the whole process; and our\u0000mapping function, utilizing Cayley parameterization, can be applied in both\u0000directions with low computational cost. Our method uniformly samples and\u0000computes a discrete volume measure of a Cartesian configuration space of point\u0000sets satisfying systems of distance inequality constraints. The systems belong\u0000to a large natural class whose feasible configuration spaces are effectively\u0000lower dimensional subsets of high dimensional ambient space. Their topological\u0000complexity makes discrete volume computation challenging, yet necessary in\u0000several application scenarios including free energy calculation in soft matter\u0000assembly modeling. The algorithm runs in linear time and empirically sub-linear\u0000space in the number of grid hypercubes (used to define the discrete volume\u0000measure) textit{that intersect} the configuration space. In other words, the\u0000number of wasted grid cube visits is insignificant compared to prevailing\u0000methods typically based on gradient descent. Specifically, the traversal stays\u0000within the feasible configuration space by viewing it as a branched covering,\u0000using a recent theory of Cayley or distance coordinates to convexify the base\u0000space, and by employing a space-efficient, frontier hypercube traversal data\u0000structure. A software implementation and comparison with existing methods is\u0000provided.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Image Triangulation Using the Sobel Operator for Vertex Selection 使用 Sobel 运算符选择顶点的图像三角剖分法

arXiv - CS - Computational Geometry Pub Date : 2024-08-28 DOI: arxiv-2408.16112

Olivia Laske, Lori Ziegelmeier

引用次数: 0

Approximation Algorithms for Minimum Sum of Moving-Distance and Opening-Costs Target Coverage Problem 最小移动距离和开局成本目标覆盖问题的近似算法

arXiv - CS - Computational Geometry Pub Date : 2024-08-25 DOI: arxiv-2408.13797

Lei Zhao, Zhao Zhang

引用次数: 0

Critical Point Extraction from Multivariate Functional Approximation 从多元函数近似中提取临界点

arXiv - CS - Computational Geometry Pub Date : 2024-08-23 DOI: arxiv-2408.13193

Guanqun Ma, David Lenz, Tom Peterka, Hanqi Guo, Bei Wang

引用次数: 0

Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform External Forces 靶向给药：利用均匀外力收集颗粒群的算法方法

arXiv - CS - Computational Geometry Pub Date : 2024-08-19 DOI: arxiv-2408.09729

Aaron T. Becker, Sándor P. Fekete, Li Huang, Phillip Keldenich, Linda Kleist, Dominik Krupke, Christian Rieck, Arne Schmidt

{"title":"Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform External Forces","authors":"Aaron T. Becker, Sándor P. Fekete, Li Huang, Phillip Keldenich, Linda Kleist, Dominik Krupke, Christian Rieck, Arne Schmidt","doi":"arxiv-2408.09729","DOIUrl":"https://doi.org/arxiv-2408.09729","url":null,"abstract":"We investigate algorithmic approaches for targeted drug delivery in a\u0000complex, maze-like environment, such as a vascular system. The basic scenario\u0000is given by a large swarm of micro-scale particles (''agents'') and a\u0000particular target region (''tumor'') within a system of passageways. Agents are\u0000too small to contain on-board power or computation and are instead controlled\u0000by a global external force that acts uniformly on all particles, such as an\u0000applied fluidic flow or electromagnetic field. The challenge is to deliver all\u0000agents to the target region with a minimum number of actuation steps. We provide a number of results for this challenge. We show that the\u0000underlying problem is NP-complete, which explains why previous work did not\u0000provide provably efficient algorithms. We also develop several algorithmic\u0000approaches that greatly improve the worst-case guarantees for the number of\u0000required actuation steps. We evaluate our algorithmic approaches by numerous\u0000simulations, both for deterministic algorithms and searches supported by deep\u0000learning, which show that the performance is practically promising.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Polynomial 2D Green Coordinates for High-order Cages 高阶笼的多项式二维绿色坐标

arXiv - CS - Computational Geometry Pub Date : 2024-08-13 DOI: arxiv-2408.06831

Shibo Liu, Ligang Liu, Xiao-Ming Fu

引用次数: 0

Searching in Euclidean Spaces with Predictions 用预测在欧几里得空间中搜索

arXiv - CS - Computational Geometry Pub Date : 2024-08-09 DOI: arxiv-2408.04964

Sergio Cabello, Panos Giannopoulos

引用次数: 0

Size Should not Matter: Scale-invariant Stress Metrics 大小无关紧要：规模不变的应力指标

arXiv - CS - Computational Geometry Pub Date : 2024-08-08 DOI: arxiv-2408.04688

Reyan Ahmed, Cesim Erten, Stephen Kobourov, Jonah Lotz, Jacob Miller, Hamlet Taraz

{"title":"Size Should not Matter: Scale-invariant Stress Metrics","authors":"Reyan Ahmed, Cesim Erten, Stephen Kobourov, Jonah Lotz, Jacob Miller, Hamlet Taraz","doi":"arxiv-2408.04688","DOIUrl":"https://doi.org/arxiv-2408.04688","url":null,"abstract":"The normalized stress metric measures how closely distances between vertices\u0000in a graph drawing match the graph-theoretic distances between those vertices.\u0000It is one of the most widely employed quality metrics for graph drawing, and is\u0000even the optimization goal of several popular graph layout algorithms. However,\u0000normalized stress can be misleading when used to compare the outputs of two or\u0000more algorithms, as it is sensitive to the size of the drawing compared to the\u0000graph-theoretic distances used. Uniformly scaling a layout will change the\u0000value of stress despite not meaningfully changing the drawing. In fact, the\u0000change in stress values can be so significant that a clearly better layout can\u0000appear to have a worse stress score than a random layout. In this paper, we\u0000study different variants for calculating stress used in the literature (raw\u0000stress, normalized stress, etc.) and show that many of them are affected by\u0000this problem, which threatens the validity of experiments that compare the\u0000quality of one algorithm to that of another. We then experimentally justify one\u0000of the stress calculation variants, scale-normalized stress, as one that fairly\u0000compares drawing outputs regardless of their size. We also describe an\u0000efficient computation for scale-normalized stress and provide an open source\u0000implementation.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0