Sergio Cabello , Arun Kumar Das , Sandip Das , Joydeep Mukherjee
{"title":"Finding a largest-area triangle in a terrain in near-linear time","authors":"Sergio Cabello , Arun Kumar Das , Sandip Das , Joydeep Mukherjee","doi":"10.1016/j.comgeo.2025.102171","DOIUrl":null,"url":null,"abstract":"<div><div>A terrain is an <em>x</em>-monotone polygon whose lower boundary is a single line segment. We present an algorithm to find in a terrain a triangle of largest area in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> time, where <em>n</em> is the number of vertices defining the terrain. The best previous algorithm for this problem has a running time of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":"128 ","pages":"Article 102171"},"PeriodicalIF":0.4000,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Geometry-Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0925772125000094","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A terrain is an x-monotone polygon whose lower boundary is a single line segment. We present an algorithm to find in a terrain a triangle of largest area in time, where n is the number of vertices defining the terrain. The best previous algorithm for this problem has a running time of .
期刊介绍:
Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems.
Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.