Finding a largest-area triangle in a terrain in near-linear time

Cabello, Sergio (author), Das, Arun Kumar (author), Das, Sandip (author), Mukherjee, Joydeep (author)

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 $O(n\log n)$ time, where $n$ is the number of vertices defining the terrain. The best previous algorithm for this problem has a running time of $O(n^2)$.

• Language: English
• Keywords: terrain, inclusion problem, geometric optimisation, hereditary segment tree
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 13 str.
• Numbering: Vol. 128, art. 102171
• PID: 20.500.12556/RUL-167822
• UDC: 004.92:519.8
• ISSN on article: 0925-7721
• DOI: 10.1016/j.comgeo.2025.102171
• COBISS.SI-ID: 228678147
• Publication date in RUL: 13.03.2025

Record is a part of a journal

• Title: Computational geometry
• Shortened title: Comput. geom.
• Publisher: Elsevier
• ISSN: 0925-7721
• COBISS.SI-ID: 14903301

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.