Handbook of Discrete and Computational Geometry, 2nd Ed.最新文献

Polyominoes Polyominoes

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2020-06-30 DOI: 10.1201/9781420035315.ch15

S. Golomb, D. Klarner

引用次数: 131

Linear programming 线性规划

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2018-10-03 DOI: 10.1201/9781420035315.pt6

M. Dyer, N. Megiddo, E. Welzl

引用次数: 0

The discrepancy method in computational geometry 计算几何中的差异法

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch44

B. Chazelle

{"title":"The discrepancy method in computational geometry","authors":"B. Chazelle","doi":"10.1201/9781420035315.ch44","DOIUrl":"https://doi.org/10.1201/9781420035315.ch44","url":null,"abstract":"Discrepancy theory investigates how uniform nonrandom structures can be. For example, given n points in the plane, how should we color them red and blue so as to minimize the difference between the number of red points and the number of blue ones within any disk? Or, how should we place n points in the unit square so that the number of points that lie within any given triangle in the square is as close as possible to n times the area of the triangle? Questions of this nature have direct relevance to computational geometry for two reasons. One of them is their close association with the problem of derandomizing probabilistic algorithms. Such algorithms are often based on random sampling and discrepancy theory provides tools for carrying out the sampling deterministically. This has led to the intriguing fact that virtually all of the important problems in low-dimensional computational geometry can be solved as efficiently deterministically as probabilistically. The second application of discrepancy theory to computational geometry is in the area of lower bounds for multidimensional searching. The complexity of these problems is often tied to spectral properties of geometric set systems, which themselves lie at the heart of geometric discrepancy theory.","PeriodicalId":156768,"journal":{"name":"Handbook of Discrete and Computational Geometry, 2nd Ed.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131304751","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: 27

Two computational geometry libraries: LEDA and CGAL 两个计算几何库:LEDA和CGAL

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch65

Lutz Kettner, S. Näher

{"title":"Two computational geometry libraries: LEDA and CGAL","authors":"Lutz Kettner, S. Näher","doi":"10.1201/9781420035315.ch65","DOIUrl":"https://doi.org/10.1201/9781420035315.ch65","url":null,"abstract":"Over the past decades, two major software libraries that support a wide range of geometric computing have been developed: Leda, the Library of Efficient Data Types and Algorithms, and Cgal, the Computational Geometry Algorithms Library. We start with an introduction of common aspects of both libraries and major differences. We continue with sections that describe each library in detail. Both libraries are written in C++. Leda is based on the object-oriented paradigm and Cgal is based on the generic programming paradigm. They provide a collection of flexible, efficient, and correct software components for computational geometry. Users should be able to easily include existing functionality into their programs. Additionally, both libraries have been designed to serve as platforms for the implementation of new algorithms. Correctness is of crucial importance for a library, even more so in the case of geometric algorithms where correctness is harder to achieve than in other areas of software construction. Two well-known reasons are the exact arithmetic assumption and the nondegeneracy assumption that are often used in geometric algorithms. However, both assumptions usually do not hold: floating point arithmetic is not exact and inputs are frequently degenerate. See Chapter 45 for details.","PeriodicalId":156768,"journal":{"name":"Handbook of Discrete and Computational Geometry, 2nd Ed.","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123026435","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: 30

Geometry and Topology of Polygonal Linkages 多边形连杆的几何与拓扑

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch9

R. Connelly, E. Demaine

引用次数: 42

Low-Distortion Embeddings of Finite Metric Spaces 有限度量空间的低失真嵌入

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch8

P. Indyk, J. Matoušek

引用次数: 217

Geometric Graph Theory 几何图论

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch10

J. Pach

引用次数: 70

Computation of robust statistics 鲁棒统计量的计算

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch57

P. Rousseeuw, Anja Struyf

引用次数: 2

Biological applications of computational topology 计算拓扑的生物学应用

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch63

H. Edelsbrunner

引用次数: 18

Surface simplification and 3D geometry compression 表面简化和三维几何压缩

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 2004-04-13 DOI: 10.1201/9781420035315.ch54

J. Rossignac

引用次数: 23